• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Positions and surfaces of a knot

Research Project

Project/Area Number 23540105
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionKomazawa University

Principal Investigator

OZAWA Makoto  駒澤大学, 総合教育研究部, 准教授 (50308160)

Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords結び目 / ハンドル体 / 橋分解 / トンネル数 / 本質的曲面 / Neuwirth予想 / ザイフェルト曲面 / デーン手術 / 曲面 / 位置
Research Abstract

(1) In a joint work with Kazuto Takao, we showed that there exists a 3-bridge knot with 4-bridge destabilized bridge position.
(2) In a joint work with Atsushi Ishii and Kengo Kishimoto, for a handlebody-knot whose exterior is boundary-irreducible, there exists a unique set of 2-decomposing spheres which decompose local 1-handles up to isotopy and annulus-moves. In a joint work with Mario Eudave-Munoz, we characterized tunnel number 1 genus 2 handlebody-knots. In a joint work with Yuya Koda, we gave a classification of essential disks, annuli and tori in the exterior of a genus 2 handlebody-knot.
(3) We showed that uniformly twisted knots satisfy the Neuwirth conjecture.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (63 results)

All 2014 2013 2012 2011 Other

All Journal Article (10 results) (of which Peer Reviewed: 10 results) Presentation (52 results) (of which Invited: 1 results) Remarks (1 results)

  • [Journal Article] A locally minimal, but not globally minimal bridge position of a knot2013

    • Author(s)
      M. Ozawa , K. Takao
    • Journal Title

      Math. Proc. Cambridge Philos. Soc

      Volume: Vol.155, no.1 Issue: 1 Pages: 181-190

    • DOI

      10.1017/s0305004113000182

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] The representativity of pretzel knots2013

    • Author(s)
      M. Ozawa
    • Journal Title

      J. Knot Theory and its Ramifications

      Volume: Vol.21, no.2 Issue: 02 Pages: 1250016-1250016

    • DOI

      10.1142/s0218216511009716

    • Related Report
      2013 Final Research Report 2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] On the Neuwirth conjecture for knots2012

    • Author(s)
      M. Ozawa, J. H. Rubinstein
    • Journal Title

      Communications in Analysis and Geometry

      Volume: Vol.20, no.5 Issue: 5 Pages: 1019-1060

    • DOI

      10.4310/cag.2012.v20.n5.a5

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Bridge position and the representativity of spatial graphs2012

    • Author(s)
      M. Ozawa
    • Journal Title

      Topology and its Appl

      Volume: Vol.159, no.4 Issue: 4 Pages: 936-947

    • DOI

      10.1016/j.topol.2011.11.026

    • Related Report
      2013 Final Research Report 2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Essential state surfaces for knots and links2012

    • Author(s)
      Makoto Ozawa
    • Journal Title

      J. Austral. Math. Soc.

      Volume: 未定(掲載確定)

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Essential state surfaces for knots and links2011

    • Author(s)
      M. Ozawa
    • Journal Title

      J. Austral. Math. Soc

      Volume: Vol.91, no.3 Issue: 3 Pages: 391-404

    • DOI

      10.1017/s1446788712000055

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Nonminimal bridge positions of torus knots are stabilized2011

    • Author(s)
      M. Ozawa
    • Journal Title

      Math. Proc. Cambridge Philos. Soc

      Volume: Vol.151, no.2 Issue: 2 Pages: 307-317

    • DOI

      10.1017/s0305004111000235

    • Related Report
      2013 Final Research Report 2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Composite tunnel number one genus two handlebody-knots

    • Author(s)
      M. Eudave-Munoz , M. Ozawa
    • Journal Title

      Bol. Soc. Mat. Mexicana

      Volume: (掲載予定)

    • URL

      http://arxiv.org/abs/1305.3410

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Knotted handle decomposing spheres for handlebody-knots

    • Author(s)
      A. Ishii, K. Kishimoto, M. Ozawa
    • Journal Title

      J. Math. Soc. Japan

      Volume: (掲載予定)

    • NAID

      130004927769

    • URL

      http://arxiv.org/abs/1211.4458

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Essential surfaces of non-negative Euler characteristic in genus two handlebody exteriors

    • Author(s)
      Y. Koda , M. Ozawa
    • Journal Title

      Trans. Amer. Math. Soc

      Volume: (掲載予定)

    • URL

      http://arxiv.org/abs/1212.5928

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Presentation] Dehn surgery and Seifert surface system, (joint work with Koya Shimokawa)2014

    • Author(s)
      Makoto Ozawa
    • Organizer
      日本数学会2014年度年会
    • Place of Presentation
      学習院大学
    • Year and Date
      2014-03-15
    • Related Report
      2013 Final Research Report
  • [Presentation] Destabilized bridge spheres of knots, (joint work with Yeonhee Jang, Tsuyoshi Kobayashi, Kazuto Takao)2014

    • Author(s)
      Kazuto Takao
    • Organizer
      第8回福岡・札幌 幾何学セミナー
    • Place of Presentation
      九州大学
    • Year and Date
      2014-02-20
    • Related Report
      2013 Final Research Report
  • [Presentation] Dehn surgery and Seifert surface system, (joint work with Koya Shimokawa)2014

    • Author(s)
      Makoto Ozawa
    • Organizer
      Seminari di Geometria
    • Place of Presentation
      Universita di Pisa
    • Year and Date
      2014-02-19
    • Related Report
      2013 Final Research Report
  • [Presentation] Coiled surfaces for knots and links, (joint work with Koya Shimokawa)2013

    • Author(s)
      Makoto Ozawa
    • Organizer
      東北結び目セミナー2013
    • Place of Presentation
      東北大学
    • Year and Date
      2013-10-26
    • Related Report
      2013 Final Research Report
  • [Presentation] Essential surfaces of non-negative Euler characteristic in genus two handlebody exteriors, (joint work with Yuya Koda)2013

    • Author(s)
      Makoto Ozawa
    • Organizer
      International Conference on Topology and Geometry 2013
    • Place of Presentation
      島根大学
    • Year and Date
      2013-09-03
    • Related Report
      2013 Final Research Report
  • [Presentation] Essential surfaces of non-negative Euler characteristic in genus two handlebody exteriors, (joint work with Yuya Koda)2013

    • Author(s)
      Makoto Ozawa
    • Organizer
      International Workshop on Spatial Graphs 2013
    • Place of Presentation
      東京女子大学
    • Year and Date
      2013-08-15
    • Related Report
      2013 Final Research Report
  • [Presentation] Destabilized bridge spheres of knots, (joint work with Yeonhee Jang, Tsuyoshi Kobayashi, Kazuto Takao)2013

    • Author(s)
      Kazuto Takao
    • Organizer
      Friday Seminar on Knot Theory
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2013-07-12
    • Related Report
      2013 Final Research Report
  • [Presentation] Essential surfaces of non-negative Euler characteristic in genus two handlebody exteriors, (joint work with Yuya Koda), Low-dimensional Topology and Geometry in Toulouse2013

    • Author(s)
      Makoto Ozawa
    • Place of Presentation
      Toulouse Mathematics Institute
    • Year and Date
      2013-06-25
    • Related Report
      2013 Final Research Report
  • [Presentation] Coexistence of coiled surfaces and spanning surfaces for knots and links2013

    • Author(s)
      Makoto Ozawa
    • Organizer
      日本数学会2013年度年会
    • Place of Presentation
      京都大学
    • Year and Date
      2013-03-20
    • Related Report
      2013 Final Research Report 2012 Research-status Report
  • [Presentation] A destabilized bridge sphere of bridge number arbitrarily higher than the bridge number of the knot, (joint work with Kazuto Takao)2013

    • Author(s)
      Kazuto Takao
    • Organizer
      日本数学会2013年度年会
    • Place of Presentation
      京都大学
    • Year and Date
      2013-03-20
    • Related Report
      2013 Final Research Report
  • [Presentation] Coexistence of coiled surfaces and spanning surfaces for knots and links, 結び目の数学V2012

    • Author(s)
      Makoto Ozawa
    • Place of Presentation
      早稲田大学
    • Year and Date
      2012-12-26
    • Related Report
      2013 Final Research Report
  • [Presentation] Coexistence of coiled surfaces and spanning surfaces for knots and links2012

    • Author(s)
      Makoto Ozawa
    • Organizer
      School on Knot Theory and 3-Manifolds
    • Place of Presentation
      Centro de Investigación en Matemáticas
    • Year and Date
      2012-12-20
    • Related Report
      2013 Final Research Report
  • [Presentation] Estimating Hempel distances and locally minimal bridge decompositions of knots, (joint work with Kazuto Takao)2012

    • Author(s)
      Kazuto Takao
    • Organizer
      葉層構造と微分同相群2012研究集会
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Year and Date
      2012-11-02
    • Related Report
      2013 Final Research Report
  • [Presentation] On the Neuwirth conjecture for knots, (joint work with J. Hyam Rubinstein)2012

    • Author(s)
      Makoto Ozawa
    • Organizer
      東北結び目セミナー2012
    • Place of Presentation
      山形大学
    • Year and Date
      2012-10-13
    • Related Report
      2013 Final Research Report
  • [Presentation] Composite handlebody-knots, (joint work with A. Ishii and K. Kishimoto, Mario Eudave-Munoz)2012

    • Author(s)
      Makoto Ozawa
    • Organizer
      Seminari di Geometria
    • Place of Presentation
      Universita di Pisa
    • Year and Date
      2012-09-05
    • Related Report
      2013 Final Research Report
  • [Presentation] A locally minimal, but not globally minimal bridge position of a knot, (joint work with Kazuto Takao)2012

    • Author(s)
      Kazuto Takao
    • Organizer
      Workshop on Topology and Geometry -Heegaard splittings of 3-manifolds II-
    • Place of Presentation
      広島大学
    • Year and Date
      2012-08-04
    • Related Report
      2013 Final Research Report
  • [Presentation] A locally minimal, but not globally minimal bridge position of a knot, (joint work with Kazuto Takao)2012

    • Author(s)
      Makoto Ozawa
    • Organizer
      Mini-symposium "Knot Theory and its ramifications" at The 6th European Congress of Mathematics
    • Place of Presentation
      Jagiellonian University
    • Year and Date
      2012-07-05
    • Related Report
      2013 Final Research Report
  • [Presentation] The representativity of knots2012

    • Author(s)
      Makoto Ozawa
    • Organizer
      日本数学会2012年度年会
    • Place of Presentation
      東京理科大学
    • Year and Date
      2012-03-26
    • Related Report
      2013 Final Research Report 2011 Research-status Report
  • [Presentation] Nonminimal bridge positions of torus knots are stabilized2012

    • Author(s)
      Makoto Ozawa
    • Organizer
      日本数学会2012年度年会
    • Place of Presentation
      東京理科大学
    • Year and Date
      2012-03-26
    • Related Report
      2013 Final Research Report
  • [Presentation] Composite tunnel number one genus two handlebody-knots, (joint work with Mario Eudave-Munoz)2012

    • Author(s)
      Mario Eudave-Munoz
    • Organizer
      46th Annual Spring Topology and Dynamics Conference
    • Place of Presentation
      Univerisdad Nacional Autonoma de Mexico
    • Year and Date
      2012-03-23
    • Related Report
      2013 Final Research Report
  • [Presentation] Composite handlebody-knots, (joint work with A. Ishii and K. Kishimoto, Mario Eudave-Munoz), 結び目理論の展望2012

    • Author(s)
      Makoto Ozawa
    • Place of Presentation
      早稲田大学
    • Year and Date
      2012-03-17
    • Related Report
      2013 Final Research Report
  • [Presentation] On the Neuwirth conjecture for knots, (joint work with J. Hyam Rubinstein)2012

    • Author(s)
      Makoto Ozawa
    • Place of Presentation
      九州大学西新プラザ
    • Year and Date
      2012-03-12
    • Related Report
      2013 Final Research Report
  • [Presentation] Composite handlebody-knots, (joint work with A. Ishii and K. Kishimoto, Mario Eudave-Munoz), Low dimensional topology and number theory IV2012

    • Author(s)
      Makoto Ozawa
    • Organizer
      Spring Workshop 2011 on Low-Dimensional Topology and its Ramifications, Joint Workshop 「ハンドル体結び目とその周辺IV」
    • Place of Presentation
      名城大学名駅サテライト
    • Year and Date
      2012-03-03
    • Related Report
      2013 Final Research Report
  • [Presentation] Estimation for Hempel distances and a nonminimal unstabilzed bridge decomposition of a knot, (partially joint work with Kazuto Takao)2012

    • Author(s)
      Kazuto Takao
    • Organizer
      Spring Workshop 2011 on Low-Dimensional Topology and its Ramifications, Joint Workshop 「ハンドル体結び目とその周辺IV」
    • Place of Presentation
      名城大学名駅サテライト
    • Year and Date
      2012-03-02
    • Related Report
      2013 Final Research Report
  • [Presentation] A locally minimal, but not globally minimal bridge position of a knot, (joint work with Kazuto Takao)2012

    • Author(s)
      Makoto Ozawa
    • Organizer
      Seminario de Topologia en Dimensiones Bajas
    • Place of Presentation
      Universidad Nacional Autonoma de Mexico
    • Year and Date
      2012-02-17
    • Related Report
      2013 Final Research Report
  • [Presentation] A locally minimal, but not globally minimal2012

    • Author(s)
      Makoto Ozawa
    • Organizer
      Seminario de Topologia en Dimensiones Bajas(招待講演)
    • Place of Presentation
      Universidad Nacional Autonoma de Mexico
    • Related Report
      2011 Research-status Report
  • [Presentation] Composite handlebody-knots2012

    • Author(s)
      Makoto Ozawa
    • Organizer
      ハンドル体結び目とその周辺 IV(招待講演)
    • Place of Presentation
      名城大学名駅サテライト
    • Related Report
      2011 Research-status Report
  • [Presentation] On the Neuwirth conjecture for knots2012

    • Author(s)
      Makoto Ozawa
    • Organizer
      Low dimensional topology and number theory IV(招待講演)
    • Place of Presentation
      九州大学西新プラザ
    • Related Report
      2011 Research-status Report
  • [Presentation] Composite handlebody-knots2012

    • Author(s)
      Makoto Ozawa
    • Organizer
      結び目理論の展望(招待講演)
    • Place of Presentation
      早稲田大学
    • Related Report
      2011 Research-status Report
  • [Presentation] Nonminimal bridge positions of torus knots2012

    • Author(s)
      Makoto Ozawa
    • Organizer
      日本数学会2012年度年会
    • Place of Presentation
      東京理科大学
    • Related Report
      2011 Research-status Report
  • [Presentation] Nonminimal bridge positions of torus knots are stabilized, 「結び目の数学IV」2011

    • Author(s)
      Makoto Ozawa
    • Place of Presentation
      東京女子大学
    • Year and Date
      2011-12-26
    • Related Report
      2013 Final Research Report
  • [Presentation] Bridge presentations of knots, 「El Seminario de Topologia en Dimensiones Bajas」2011

    • Author(s)
      Makoto Ozawa
    • Place of Presentation
      Universidad Nacional Autonoma de Mexico
    • Year and Date
      2011-08-19
    • Related Report
      2013 Final Research Report
  • [Presentation] On the Neuwirth conjecture for knots, (joint work with J. Hyam Rubinstein)2011

    • Author(s)
      Makoto Ozawa
    • Organizer
      東京女子大学トポロジーセミナー
    • Place of Presentation
      東京女子大学
    • Year and Date
      2011-05-21
    • Related Report
      2013 Final Research Report
  • [Presentation] On the Neuwirth conjecture for knots2011

    • Author(s)
      Makoto Ozawa
    • Organizer
      東京女子大学トポロジーセミナー(招待講演)
    • Place of Presentation
      東京女子大学
    • Related Report
      2011 Research-status Report
  • [Presentation] Bridge presentations of knots2011

    • Author(s)
      Makoto Ozawa
    • Organizer
      El Seminario de Topologia en Dimensiones Bajas(招待講演)
    • Place of Presentation
      Universidad Nacional Autonoma de Mexico
    • Related Report
      2011 Research-status Report
  • [Presentation] Nonminimal bridge positions of torus knots2011

    • Author(s)
      Makoto Ozawa
    • Organizer
      結び目の数学IV
    • Place of Presentation
      東京女子大学
    • Related Report
      2011 Research-status Report
  • [Presentation] Essential surfaces of non-negative Euler characteristic in genus two handlebody exteriors

    • Author(s)
      小沢誠
    • Organizer
      Low-dimensional Topology and Geometry in Toulouse
    • Place of Presentation
      Toulouse Mathematics Institute
    • Related Report
      2013 Annual Research Report
  • [Presentation] Destabilized bridge spheres of knots

    • Author(s)
      高尾和人
    • Organizer
      Friday Seminar on Knot Theory
    • Place of Presentation
      大阪市立大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] Essential surfaces of non-negative Euler characteristic in genus two handlebody exteriors

    • Author(s)
      小沢誠
    • Organizer
      International Workshop on Spatial Graphs 2013
    • Place of Presentation
      東京女子大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] Essential surfaces of non-negative Euler characteristic in genus two handlebody exteriors

    • Author(s)
      小沢誠
    • Organizer
      International Conference on Topology and Geometry 2013
    • Place of Presentation
      島根大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] Coiled surfaces for knots and links

    • Author(s)
      小沢誠
    • Organizer
      東北結び目セミナー2013
    • Place of Presentation
      東北大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] Dehn surgery and Seifert surface system

    • Author(s)
      小沢誠
    • Organizer
      Seminari di Geometria
    • Place of Presentation
      Universita di Pisa
    • Related Report
      2013 Annual Research Report
  • [Presentation] Destabilized bridge spheres of knots

    • Author(s)
      高尾和人
    • Organizer
      第8回 福岡・札幌 幾何学セミナー
    • Place of Presentation
      九州大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] Dehn surgery and Seifert surface system

    • Author(s)
      小沢誠
    • Organizer
      日本数学会2014年度年会
    • Place of Presentation
      学習院大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] A destabilized bridge sphere of bridge number arbitrarily higher than the bridge number of the knot

    • Author(s)
      Kazuto Takao
    • Organizer
      日本数学会2013年度年会
    • Place of Presentation
      京都大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Coexistence of coiled surfaces and spanning surfaces for knots and links

    • Author(s)
      Makoto Ozawa
    • Organizer
      結び目の数学 V
    • Place of Presentation
      早稲田大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Coexistence of coiled surfaces and spanning surfaces for knots and links

    • Author(s)
      Makoto Ozawa
    • Organizer
      School on Knot Theory and 3-Manifolds
    • Place of Presentation
      Centro de Investigacion en Matematicas
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Estimating Hempel distances and locally minimal bridge decompositions of knots

    • Author(s)
      Kazuto Takao
    • Organizer
      葉層構造と微分同相群2012研究集会
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Related Report
      2012 Research-status Report
  • [Presentation] On the Neuwirth conjecture for knots

    • Author(s)
      Makoto Ozawa
    • Organizer
      東北結び目セミナー2012
    • Place of Presentation
      山形大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Composite handlebody-knots

    • Author(s)
      Makoto Ozawa
    • Organizer
      Seminari di Geometria
    • Place of Presentation
      Universita di Pisa
    • Related Report
      2012 Research-status Report
  • [Presentation] A locally minimal, but not globally minimal bridge position of a knot

    • Author(s)
      Kazuto Takao
    • Organizer
      Workshop on Topology and Geometry ―Heegaard splittings of 3-manifolds II―
    • Place of Presentation
      広島大学
    • Related Report
      2012 Research-status Report
  • [Presentation] A locally minimal, but not globally minimal bridge position of a knot

    • Author(s)
      Makoto Ozawa
    • Organizer
      Mini-symposium "Knot Theory and its ramifications" at The 6th European Congress of Mathematics
    • Place of Presentation
      Jagiellonian University
    • Related Report
      2012 Research-status Report
  • [Remarks]

    • URL

      http://www.komazawa-u.ac.jp/~w3c/

    • Related Report
      2013 Final Research Report

URL: 

Published: 2011-08-05   Modified: 2019-07-29  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi