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Topology of stable mappings and diagrams of four-manifolds

Research Project

Project/Area Number 26800027
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Geometry
Research InstitutionKeio University (2016-2017)
Hokkaido University (2014-2015)

Principal Investigator

Hayano Kenta  慶應義塾大学, 理工学部(矢上), 講師 (20722606)

Project Period (FY) 2014-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords安定写像 / 写像類群 / 消滅サイクル / trisection / モノドロミー / シンプレクティック多様体 / レフシェッツペンシル / 4次元トーラス / 偏極つきアーベル曲面 / 4次元多様体
Outline of Final Research Achievements

The results obtained in the project are followings.
It is known that total spaces of torus bundles over the torus with sections admit genus-3 Lefschetz pencils. In this project we first determine vanishing cycles of holomorphic pencils on the four-torus. We further construct Lefschetz pencils on manifolds homeomorphic to total spaces of torus bundles over the torus.
Recently, Gay and Kirby defined a trisection, which gives rise to a diagram describing a four-manifold. Trisections are related to stable mappings from four-manifolds to the plane. In analyzing stable mappings, Baykur and Saeki introduced a notion of simplified trisections and gave several examples of them. Relying on the theory of mapping class groups of surfaces, we give an algorithm to obtain diagrams associated with simplified trisections.

Report

(5 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (23 results)

All 2018 2017 2016 2015 2014 Other

All Int'l Joint Research (1 results) Journal Article (5 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 5 results,  Acknowledgement Compliant: 2 results) Presentation (15 results) (of which Int'l Joint Research: 2 results,  Invited: 7 results) Remarks (2 results)

  • [Int'l Joint Research] マサチューセッツ大学(米国)

    • Related Report
      2017 Annual Research Report
  • [Journal Article] Topology of holomorphic Lefschetz pencils on the four-torus2018

    • Author(s)
      Noriyuki Hamada and Kenta Hayano
    • Journal Title

      Algebraic & Geometric Topology

      Volume: 18-3 Issue: 3 Pages: 1515-1572

    • DOI

      10.2140/agt.2018.18.1515

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Multisections of Lefschetz fibrations and topology of symplectic 4-manifolds2016

    • Author(s)
      Kenta Hayano and Refik Inanc Baykur
    • Journal Title

      Geometry & Topology

      Volume: 未定

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Hurwitz equivalence for Lefschetz fibrations and their multisections2016

    • Author(s)
      Kenta Hayano and Refik Inanc Baykur
    • Journal Title

      AMS series in Contemporary Mathematics, the Proceedings of the XIII International Workshop on Real and Complex Singularities

      Volume: 未定

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] C∞-logarithmic transformations and generalized complex structures2015

    • Author(s)
      Ryushi Goto and Kenta Hayano
    • Journal Title

      Journal of Symplectic Geometry

      Volume: 未定

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] A new aspect of the Arnold invariant J+ from a global viewpoint2015

    • Author(s)
      Kenta Hayano and Noboru Ito
    • Journal Title

      Indiana University Mathematics Journal

      Volume: 未定

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Presentation] Topology of holomorphic Lefschetz pencils on the four-torus2017

    • Author(s)
      早野健太
    • Organizer
      Branched Coverings, Degenerations, and Related Topics 2017
    • Place of Presentation
      東北学院大学(宮城県、多賀城市)
    • Year and Date
      2017-03-07
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] New counterexamples to Stipsicz's conjecture on fiber-sum indecomposable Lefschetz fibrations2017

    • Author(s)
      早野 健太
    • Organizer
      Four Dimensional Topology
    • Related Report
      2017 Annual Research Report
  • [Presentation] On diagrams of simplified trisections and mapping class groups2017

    • Author(s)
      早野 健太
    • Organizer
      Local and global study of singularity theory of differentiable maps
    • Related Report
      2017 Annual Research Report
  • [Presentation] Topology of Lefschetz pencils on symplectic Calabi-Yau 4-manifolds with positive b_12016

    • Author(s)
      早野健太
    • Organizer
      リーマン面に関連する位相幾何学
    • Place of Presentation
      東京大学(東京都、目黒区)
    • Year and Date
      2016-09-04
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Topology of holomorphic Lefschetz pencils on the four torus2016

    • Author(s)
      Kenta Hayano
    • Organizer
      The 4th Workshop "Complex Geometry and Lie Groups"
    • Place of Presentation
      奈良女子大学(奈良県・奈良市)
    • Year and Date
      2016-03-24
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Uniqueness of holomorphic Lefschetz pencils on the four torus2016

    • Author(s)
      早野 健太
    • Organizer
      微分トポロジー16
    • Place of Presentation
      筑波大学(茨城県・つくば市)
    • Year and Date
      2016-03-21
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] 4次元トーラス上のレフシェッツペンシルのモノドロミーについて2016

    • Author(s)
      早野 健太
    • Organizer
      接触構造、特異点、微分方程式及びその周辺
    • Place of Presentation
      金沢大学サテライトプラザ(石川県・金沢市)
    • Year and Date
      2016-01-21
    • Related Report
      2015 Research-status Report
  • [Presentation] アーベル曲面上の正則レフシェッツペンシルのトポロジー2016

    • Author(s)
      早野 健太
    • Organizer
      Hurwitz action 5
    • Place of Presentation
      大阪市立大学(大阪府・大阪市)
    • Year and Date
      2016-01-11
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] Lefschetz fibrations and mapping class groups2015

    • Author(s)
      Kenta Hayano
    • Organizer
      Japanese Australian workshop on Real and Complex Singularities 6th
    • Place of Presentation
      鹿児島大学(鹿児島県・鹿児島市)
    • Year and Date
      2015-11-26
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Hurwitz equivalence for fibration structures on 4-manifolds2015

    • Author(s)
      早野 健太
    • Organizer
      拡大KOOKセミナー2015
    • Place of Presentation
      神戸大学(兵庫県・神戸市)
    • Year and Date
      2015-08-21
    • Related Report
      2015 Research-status Report
  • [Presentation] Multisections of Lefschetz fibrations and topology of symplectic 4-manifolds"2015

    • Author(s)
      早野 健太
    • Organizer
      日本数学会2015年度会
    • Place of Presentation
      明治大学(東京都)
    • Year and Date
      2015-03-23
    • Related Report
      2014 Research-status Report
  • [Presentation] Multisections of Lefschetz fibrations and topology of symplectic 4-manifolds2015

    • Author(s)
      Kenta Hayano
    • Organizer
      The tenth east sian school of knots and related topics
    • Place of Presentation
      East China Normal University(中国)
    • Year and Date
      2015-01-27
    • Related Report
      2014 Research-status Report
  • [Presentation] Multisections of Lefschetz fibrations and topology of symplectic 4-manifolds2014

    • Author(s)
      早野 健太
    • Organizer
      4次元トポロジー
    • Place of Presentation
      大阪市立大学(大阪府、大阪市)
    • Year and Date
      2014-11-22
    • Related Report
      2014 Research-status Report
  • [Presentation] Multisections of Lefschetz fibrations and mapping class groups of surfaces2014

    • Author(s)
      Kenta Hayano
    • Organizer
      The 2nd Franco-Japanese-Vietnamese Symposium on Singularities
    • Place of Presentation
      北海道大学(北海道、札幌市)
    • Year and Date
      2014-08-27
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Multisections of Lefschetz fibrations and mapping class groups of surfaces2014

    • Author(s)
      Kenta Hayano
    • Organizer
      13th International Workshop on Real and Complex Singularities
    • Place of Presentation
      ICMC USP (ブラジル)
    • Year and Date
      2014-07-30
    • Related Report
      2014 Research-status Report
  • [Remarks] Homepage of Kenta Hayano

    • URL

      http://www.math.keio.ac.jp/~k-hayano/index_en.html

    • Related Report
      2015 Research-status Report
  • [Remarks] Homepage of Kenta Hayano

    • URL

      http://www.math.sci.hokudai.ac.jp/~k-hayano/index_en.html

    • Related Report
      2014 Research-status Report

URL: 

Published: 2014-04-04   Modified: 2022-06-07  

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