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Finite surgeries on pretzel knots

Research Project

Project/Area Number 20740039
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Geometry
Research InstitutionNihon University (2010)
Nara University of Education (2008-2009)

Principal Investigator

ICHIHARA Kazuhiro  Nara University of Education, 文理学部, 准教授 (00388357)

Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords位相幾何 / 3次元多様体論 / 位相幾何学
Research Abstract

Toward the characterization of the finite surgery (i.e., Dehn surgery producing 3-manifolds with finite fundamental groups) on the knots in the 3-sphere, as a first step, we gave a complete classification of finite surgeries on Montesinos knots. Related to the main subject, also studied were Dehn surgeries yielding Seifert fibered manifolds, called Seifert surgeries, and topological properties of Montesinos knots, called boundary slope diameters and crosscap numbers.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (42 results)

All 2011 2010 2009 2008 Other

All Journal Article (18 results) (of which Peer Reviewed: 18 results) Presentation (20 results) Remarks (4 results)

  • [Journal Article] Gromov hyperbolicity and a variation of the Gordian complex2011

    • Author(s)
      市原一裕、鄭仁大
    • Journal Title

      Proceedings of Japan Academy, Ser.A Mathematical Sciences

      Volume: 87 Pages: 17-21

    • NAID

      40018702757

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Constructions of surface bundles with rank two fundamental groups2011

    • Author(s)
      市原一裕、高沢光彦
    • Journal Title

      日本大学文理学部自然科学研究所研究紀要

      Volume: 46 Pages: 321-332

    • NAID

      40018816534

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Toroidal Seifert fibered surgeries on Montesinos knots.2010

    • Author(s)
      K.Ichihara, I.D.Jong
    • Journal Title

      Comm.Anal.Geom. 18 no.3

      Pages: 579-600

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Crosscap numbers of pretzel knots.2010

    • Author(s)
      K.Ichihara, S.Mizushima
    • Journal Title

      Topology Appl. 157 no.1

      Pages: 193-201

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Toroidal Seifert fibered surgeries on Montesinos knots2010

    • Author(s)
      市原一裕、鄭仁大
    • Journal Title

      Communications in Analysis and Geometry

      Volume: 18 Pages: 579-600

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Hyperbolic sections in Seifert fibered, surface bundles.2009

    • Author(s)
      K.Ichihara, K.Motegi
    • Journal Title

      Quart.J.Math. 60 no.4

      Pages: 475-486

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Lower bounds on boundary slope diameters for Montesinos knots.2009

    • Author(s)
      K.Ichihara, S.Mizushima
    • Journal Title

      Kyungpook Math.J. 49 no.2

      Pages: 321-348

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Cyclic and finite surgeries on Montesinos knots.2009

    • Author(s)
      K.Ichihara, I.D.Jong
    • Journal Title

      Algebr.Geom.Topol. 9

      Pages: 731-742

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Cyclic and finite surgeries on Montesinos knots2009

    • Author(s)
      市原一裕, 鄭仁大
    • Journal Title

      Algebraic & Geometric Topology 9

      Pages: 731-742

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Lower bounds on boundary slope diameters on Montesinos knots2009

    • Author(s)
      市原一裕, 水嶋滋
    • Journal Title

      Kyungpook Mathematical Journal 49(2)

      Pages: 321-348

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Hyperbolic sections in Seifert fibered surface bundles2009

    • Author(s)
      市原一裕, 茂手木公彦
    • Journal Title

      Quarterly Journal of Mathematics 60(4)

      Pages: 475-486

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Crosscap numbers of pretzel knots2009

    • Author(s)
      市原一裕, 水嶋滋
    • Journal Title

      Topology and its Applications 157(1)

      Pages: 193-201

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] All exceptional surgeries on alternating knots are integral surgeries.2008

    • Author(s)
      K.Ichihara
    • Journal Title

      Algebr.Geom.Topol. 8

      Pages: 2161-2173

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] ongitudinal Seifert fibered surgeries on hyperbolic knots.2008

    • Author(s)
      K.Ichihara, Kimihiko Motegi, H-J.Song
    • Journal Title

      Bull.Nara Univ.Ed.Natur.Sci.(奈良教育大学紀要自然科学編) 57 no.2

      Pages: 21-25

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Strongly invertible knots, rational-fold branched coverings and hyperbolic spatial graphs2008

    • Author(s)
      市原一裕, 牛島顕
    • Journal Title

      Revista Matematica Complutense 21(2)

      Pages: 257-261

    • NAID

      120001778355

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Crossing number and diameter of boundary slope set of Montesinos knot2008

    • Author(s)
      市原一裕, 水嶋滋
    • Journal Title

      Communications in Analysis and Geometry 16(3)

      Pages: 565-589

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Longitudinal Seifert fibered surgeries on hyperbolic knots2008

    • Author(s)
      市原一裕, 茂手木公彦, Hyun-Jong Song
    • Journal Title

      奈良教育大学紀要自然科学編 57(2)

      Pages: 21-25

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] All exceptional surgeries on alternating knots are integral surgeries2008

    • Author(s)
      市原一裕
    • Journal Title

      Algebraic & Geometric Topology 8(4)

      Pages: 2161-2173

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] Acylindrical surfaces in 3-manifolds of genus two2011

    • Author(s)
      市原一裕
    • Organizer
      「リーマン面・不連続群」研究集会
    • Place of Presentation
      大阪国際交流センター
    • Year and Date
      2011-01-10
    • Related Report
      2010 Annual Research Report
  • [Presentation] Acylindrical surfaces in 3-manifolds of genus two2010

    • Author(s)
      市原一裕
    • Organizer
      東北結び目セミナー
    • Place of Presentation
      山形市、遊学館
    • Year and Date
      2010-10-23
    • Related Report
      2010 Annual Research Report
  • [Presentation] On exceptional surgeries on Montesinos knots2010

    • Author(s)
      K.Ichihara,I.D.Jong, S.Mizushima
    • Organizer
      International Conference Japan-Mexico on Topology and its Applications
    • Place of Presentation
      The Universidad de Colima, Colima, Mexico.
    • Year and Date
      2010-09-29
    • Related Report
      2010 Final Research Report
  • [Presentation] On exceptional surgeries on Montesinos knots2010

    • Author(s)
      Kazuhiro Ichihara
    • Organizer
      International Conference Japan-Mexico on Topology and its Applications
    • Place of Presentation
      Universidad de Colima, Colima, Mexico
    • Year and Date
      2010-09-29
    • Related Report
      2010 Annual Research Report
  • [Presentation] On exceptional surgeries on Montesinos knots2010

    • Author(s)
      Kazuhiro Ichihara
    • Organizer
      The University of Melbourne Algebra/Geometry/Topology Seminar
    • Place of Presentation
      University of Melbourne, Melbourne, Australia
    • Year and Date
      2010-08-02
    • Related Report
      2010 Annual Research Report
  • [Presentation] On exceptional surgeries on Montesinos knots2010

    • Author(s)
      市原一裕
    • Organizer
      東大トポロジー火曜セミナー
    • Place of Presentation
      東京大学駒場キャンパス
    • Year and Date
      2010-06-15
    • Related Report
      2010 Annual Research Report
  • [Presentation] On exceptional surgeries on Montesinos knots2010

    • Author(s)
      市原一裕
    • Organizer
      日大トポロジーセミナー
    • Place of Presentation
      日本大学文理学部
    • Year and Date
      2010-05-08
    • Related Report
      2010 Annual Research Report
  • [Presentation] Exceptional surgeries on alternating knots2010

    • Author(s)
      K.Ichihara
    • Organizer
      研究会「結び目と3次元多様体」
    • Place of Presentation
      慶應義塾大学
    • Year and Date
      2010-03-18
    • Related Report
      2010 Final Research Report
  • [Presentation] モンテシノス結び目に沿った例外的デーン手術について2009

    • Author(s)
      K.Ichihara
    • Organizer
      研究集会「Intelligence of Low Dimensional Topology」
    • Place of Presentation
      大阪市立大学学術情報センター
    • Year and Date
      2009-11-14
    • Related Report
      2010 Final Research Report
  • [Presentation] モンテシノス結び目に沿った例外型デーン手術について2009

    • Author(s)
      市原一裕
    • Organizer
      Intelligence of Low Dimensional Topology
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2009-11-14
    • Related Report
      2009 Annual Research Report
  • [Presentation] Boundary slopes and degeneracy slopes for knots2009

    • Author(s)
      市原一裕
    • Organizer
      東北結び目セミナー
    • Place of Presentation
      山形テルサ(山形県)
    • Year and Date
      2009-10-19
    • Related Report
      2009 Annual Research Report
  • [Presentation] モンテシノス結び目に沿った有限型デーン手術2009

    • Author(s)
      K.Ichihara
    • Organizer
      日本数学会2009年度秋期総合分科会
    • Place of Presentation
      大阪大学豊中キャンパス
    • Year and Date
      2009-09-24
    • Related Report
      2010 Final Research Report
  • [Presentation] モンテシノス結び目に沿った有限型デーン手術2009

    • Author(s)
      市原一裕
    • Organizer
      日本数学会2009年度秋期総合分科会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-24
    • Related Report
      2009 Annual Research Report
  • [Presentation] JSJ decompositions of toroidal 3-manifolds obtained by Dehn surgeries on pretzel knots2009

    • Author(s)
      市原一裕, 蒲谷祐一
    • Organizer
      トポロジーとコンピュータ2009
    • Place of Presentation
      東京工業大学
    • Year and Date
      2009-08-31
    • Related Report
      2009 Annual Research Report
  • [Presentation] Bounds on exceptional surgery slopes2009

    • Author(s)
      K.Ichihara
    • Organizer
      研究集会「The first KOOK-TAPU Joint Seminar on Knot Theory and Related Topics」
    • Place of Presentation
      大阪市立大学学術情報センター
    • Year and Date
      2009-08-19
    • Related Report
      2010 Final Research Report
  • [Presentation] Bounds on exceptional surgery slopes2009

    • Author(s)
      市原一裕
    • Organizer
      The first KOOK-TAP Joint Seminar on Knot Theory and Related Topics
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2009-08-19
    • Related Report
      2009 Annual Research Report
  • [Presentation] Seifert fibered surgeries on Moidesinos knots2009

    • Author(s)
      市原一裕, 鄭仁大, 水嶋滋
    • Organizer
      The 5th East Asian School of Knots and Related Topics
    • Place of Presentation
      Gyeongju TEMF Hotel(慶州教育文化會館), 慶州, 大韓民国
    • Year and Date
      2009-01-12
    • Related Report
      2008 Annual Research Report
  • [Presentation] Seifert fibered surgeries on Montesinos knots2008

    • Author(s)
      市原一裕, 鄭仁大, 水嶋滋
    • Organizer
      研究集会「結び目の数学」
    • Place of Presentation
      東京女子大学
    • Year and Date
      2008-12-24
    • Related Report
      2008 Annual Research Report
  • [Presentation] レンズ空間のデーン手術距離について2008

    • Author(s)
      K.Ichihara
    • Organizer
      日本数学会2008年度秋期総合分科会
    • Place of Presentation
      東京工業大学大岡山キャンパス
    • Year and Date
      2008-09-25
    • Related Report
      2010 Final Research Report
  • [Presentation] レンズ空間のデーン手術距離について2008

    • Author(s)
      市原一裕, 斎藤敏夫
    • Organizer
      日本数学会2008年度秋期総合分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-25
    • Related Report
      2008 Annual Research Report
  • [Remarks] ホームページ等

    • URL

      http://www.math.chs.nihon-u.ac.jp/~ichihara/Research/index.html

    • Related Report
      2010 Final Research Report
  • [Remarks]

    • URL

      http://www.math.chs.nihon-u.ac.jp/~ichihara/Research/index.html

    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://mailsrv.nara-edu.ac.jp/~ichihara/Research/

    • Related Report
      2009 Annual Research Report
  • [Remarks]

    • URL

      http://mailsrv.nara-edu.ac.jp/~ichihara/Research/index.html

    • Related Report
      2008 Annual Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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