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Representations of 3-manifolds and geometric informations derived from them

Research Project

Project/Area Number 12640071
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionNara Women's University

Principal Investigator

KOBAYASHI Tsuyoshi  Nara Women's U.Faculty of Sci., Professor, 理学部, 教授 (00186751)

Co-Investigator(Kenkyū-buntansha) KATAGIRI Minnyou  Nara Women's U.Faculty of Sci., Assoc.Professor, 理学部, 助教授 (60263422)
YAMASHITA Yasushi  Nara Women's U.Faculty of Sci., Assis.Professor, 理学部, 講師 (70239987)
OCHIAI Mitsuyuki  Nara Women's U.Graduate Sch., Professor, 人間文化研究科, 教授 (70016179)
Project Period (FY) 2000 – 2002
Project Status Completed (Fiscal Year 2002)
Budget Amount *help
¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 2002: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2001: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2000: ¥1,000,000 (Direct Cost: ¥1,000,000)
KeywordsHeegaard splitting / 3-manifold / knot / Tunnel number / Dehn twist / Ricci curvature / Einstein metric / Heegaard Splitting / Untelescoping / 3-manifold / Knot / knot / triangulation
Research Abstract

1. Graphic of 3-manifolds
Kobayashi make use of the graphic defined by Rubinstein-Scharlemann to give a complete classification of Heegaard splittings of the exteriors of the 2-bridge knots.
2. Local detection of strong irreducibility of Heegaard splittings by using knot exteriors
Kobayashi together with, Yo'av Rieck analyzed how strongly irreducible Heegaard splittings can intersect the exteriors of non-trivial knots in the 3-sphere and showed that such Heegaard surface intersect the knot exteriors in meridional annuli.
3. Research on Morimoto's Conjecture
Kobayashi together with Yo'av Rieckstudied about Morimoto's Conjecture concerned with the connectedsums of knots in 3-manifolds and the tunnel numbers.
4. Algorithm for decompositions of attaching homeomorphisms of Heegaard splittings into Dehn twists
Ochiai gave an algorithm for giving a decomposition of given attaching homeomorphisms of genus two Heegaard splittings into standard Dehn twists.
5. Moduli space of metrics of Riemannian manifolds
Katagiri studied about Riemannian functional via Ricci curvature and showed that Einstein metric is a critical point of this functional, however there exist critical points that are not Einstein metric. He also gave a sufficient condition for critical points to be Einstein metrics.

Report

(4 results)
  • 2002 Annual Research Report   Final Research Report Summary
  • 2001 Annual Research Report
  • 2000 Annual Research Report

Research Products

(26 results)

All Other

All Publications (26 results)

  • [Publications] Mikami Hirasawa: "Pre-taut sutured manifolds and essential laminations"Osaka J.Math. 38. 905-922 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Tsuyoshi Kobayashi: "Heegaard splitting of exteriors of two bridge knots"Geometry and Topology. 5. 609-650 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y.Sakata: "Twist Decompositions of Gluingn Homeomorphisms of Planar Heegaard Diagrams of Genus Two"Proc.Amer.Math.Soc.. 129. 559-566 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Mitsuyuki Ochiai: "Computational Decomposition of Homeomorphisms of Planar Heegaard Diagrams"Far East J.Math.Sci.. 2. 869-895 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Minnyou Katagiri: "On critical Riemannian metrics for a curvature functional on 3-manifolds"Proceedings of the Japan Academy. 78. 43-45 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y.Yamashita: "Configuration spaces of points on the circle and hyperbolic Dehn fillings II"Geometreae Dedicata. 89. 143-157 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] M.Hirasawa and T.Kobayashi: "Pre-taut sutured manifolds and essential laminations"Osaka J.Math.. 38. 905-922 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T.Kobayashi: "Heegaard splittings of exteriors of two bridge knots"Geometry and Topology. 5. 609-650 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y.Sakata, M.Ochiai, and K.Satoh: "Twist Decompositions of Gluing Homeomorphisms of Planar Heegaard Diagrams of Genus Two"PROC.AMER.MATH.SOC.. 129. 59-566 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] M.Ochiai: "Computational Decomposition of Homeomorpbisms of Planar Heegaard Diagrams"Far East J.Math.Sci. (FJMS). 2. 869-895 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] M.Katagiri: "On critical Riemannian metrics for a curvature functional on 3-manifolds"Proceedings of the Japan Academy. 78. 43-45 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y.Yamashita, H.Nishi and S.Kojima: "Configuration spaces of points on the circle and hyperbolic Dehn fillings II"Geometreae Dedicata. 89. 143-157 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Mikami Hirasawa: "Pre-taut sutured manifolds and essential laminations"Osaka J.Math.. 38. 905-922 (2001)

    • Related Report
      2002 Annual Research Report
  • [Publications] Tsuyoshi Kobayashi: "Heegaard splittings of exteriors of two bridge knots"Geometry and Topology. 5. 609-650 (2001)

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Sakata: "Twist Decompositions of Gluingn Homeomorphisms of Planar Heegaard Diagrams of Genus Two"Proc.Amer.Math.Soc.. 129. 559-566 (2001)

    • Related Report
      2002 Annual Research Report
  • [Publications] Mitsuyuki Ochiai: "Computational Decomposition of Homeomorphisms of Planar Heegaard Diagrams"Far East J.Math.Sci.. 2. 869-895 (2001)

    • Related Report
      2002 Annual Research Report
  • [Publications] Minnyou Katagiri: "On critical Riemannian metrics for a curvature functional on 3-manifolds"Proceedings of the Japan Academy. 78. 43-45 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Yamashita: "Configuration spaces of points on the circle and hyperbolic Dehn fillings II"Geometreae Dedicata. 89. 143-157 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] M.Hirasawa, T.Kobayashi: "Pre-taut Sutured Manifolds and Essential Laminations"Osaka J. Math. 38. 905-922 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] T.Kobayashi: "Heegaard Splittings of Exteriors of Two Bridge Knots"Geometry and Topology. 5. 609-650 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] T.Kobayashi,O.Saeki: "Rubinstein-Scharlemann graphic of 3-manifold as the discriminant set of a stable map"Pacific J.Math.. 195. 101-156 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] M.Hirasawa,T.Kobayashi: "Pre-taut sutured manifolds and essential laminations"Osaka J.Math.. (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] Y.Sakata,M.Ochiai,K.Satoh: "Twist Decompositions of Gluing Homeomorphisms of Planar Heegaard Diagrams of Genus Two"Proc.Amer.Math.Soc.. 129. 559-566 (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] M.Ochiai: "Computational Decomposition of Homeomorphisms of Planar Heegaard Diagrams"Far East Journal Math.Sci.. 2. 869-895 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] M.Ochiai: "Non-iterative行列演算による3次元空間における曲面の最適埋蔵法"情報処理学会論文誌. (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] M.Ochiai: "種数2の3次元閉多様体の平面的自己同相写像の分解過程の可視化"パーソナルコンピュータ利用技術協会論文誌.

    • Related Report
      2000 Annual Research Report

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Published: 2000-03-31   Modified: 2016-04-21  

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