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A homology of orbifolds and related groups

Research Project

Project/Area Number 11640071
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionShizuoka University

Principal Investigator

YOKOYAMA Misako  Shizuoka University, Science, research assistant, 理学部, 助手 (80240224)

Co-Investigator(Kenkyū-buntansha) KUMURA Hironori  Shizuoka University, Science, full-time lecturer, 理学部, 講師 (30283336)
OKUMURA Yoshihide  Shizuoka University, Science, associated professor, 理学部, 助教授 (90214080)
IZAWA Tatsuo  Shizuoka University, Science, associated professor, 理学部, 助教授 (20021941)
Project Period (FY) 1999 – 2000
Project Status Completed (Fiscal Year 2000)
Budget Amount *help
¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2000: ¥1,100,000 (Direct Cost: ¥1,100,000)
Keywordsorbifold / homology
Research Abstract

We define the PL-area of a 2-orbifold immersed in a 3-orbifold. We show that any two least area 2-orbifolds belonging to the class Ω do not intersect each other. The existence of the least area 2-orbifold is proved. And we obtain somes applications.
Waldhausen considered a certain class of 3-manifold called Haken manifolds, and classified it by their fundamental groups. Similary, Takeuchi classified a certain class of very good 3-orbifolds, and we classify much larger class of 3-orbifolds by their orbifold fundamental groups.
We introduce an orbifold composition and study their topology and the extensions and deformations of the maps between them. We obtain the theorems which yield the geometric realizations of amalgamated free products and HNN extensions of 3-orbifold fundamental groups. They are extensions of results of Feustel (1972,1973) and Feustel and Gregorac (1973).
We find spherical 2-orbifolds realizing the decomposition of the 3-orbifold fundamental groups, of which the amalgamated subgroups are isomorphic to the fundamental groups of orientable spherical 2-orbifolds. If one hypothesis fails, then there is a 3-orbifold which could not realize the given group decompositon. As an application we obatin a necessary and sufficient condition that unsplittable links embedded in S^3 are composite.

Report

(3 results)
  • 2000 Annual Research Report   Final Research Report Summary
  • 1999 Annual Research Report
  • Research Products

    (29 results)

All Other

All Publications (29 results)

  • [Publications] Y.Takeuchi & M.Yokoyama: "PL-least area 2-orbifolds and its applications to 3-orbifolds"Kyushu J.Math.. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Takeuchi & M.Yokoyama: "Waldhausen's classification theorem for 3-orbifolds"Kyushu J.Math.. 54・2. 371-401 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Takeuchi & M.Yokoyama: "The geometric realizations of the decompositions of 3-orbifold fundamental groups"Topology Appl.. 95. 129-153 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Yoshihide Okumura: "Lifting problem and its application to Riemann surfaces"Eighth International Conference on Complex Analysis. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] 奥村善英: "リーマン面上の単純閉曲線が分割曲線になるための必要十分条件"京都大学数理解析研究所講究録. 1163. 28-41 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] 奥村善英: "タイヒミュラー空間の角度変数とその応用"京都大学数理解析研究所講究録. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Hironori Kumura: "A note on the absence of eigenvalues on negatively curved manifold"Kyushu J.Math. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Keiko Chiba: "The strong paracompactness of δ-products"Scientiae Mathematicae. 2・3. 285-292 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Keiko Chiba: "Remarks on Suslin number of inverse limits"Reports of the Faculty of Science, Shizuoka University. 35. 1-5 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Takeuchi and M.Yokoyama: "PL-least area 2-orbifolds and its applications to 3-orbifolds"Kyushu J.Math.. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Takeuchi and M.Yokoyama: "Waldhausen's classification theorem for 3-orbifolds"Kyushu J.Math.. 54-2. 371-401 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Takeuchi and M.Yokoyama: "The geometric realization of the decompositions of 3-orbifold fundamental groups"Topology Appl.. 95. 129-153 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Yoshihide Okumura: "Lifting problem and its application to Riemann surfaces"Eighth International Conference on Complex Analysis. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Yoshihide Okumura: "Necessary and sufficient conditions for simple closed curves on Riemann surfaces to be separating loops"Surikaisekikenkyusho Kokyuroku. 1163(in Japanese). 28-41 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Yoshihide Okumura: "Angle variables in Teichmuller spaces and its applications"Surikaisekikenkyusho Kokyuroku. (to appear)(in Japanese).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Hironori Kumura: "A note on the absence of eigenvalues on negatively curved manifold"Kyushu J.Math.. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Keiko Chiba: "The strong paracompactness of σ-products"Scientiae Mathematicae. 2-3. 285-292 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Keiko Chiba: "Remarks on Suslin number of inverse limits"Rep.Fac.Sci., Shizuoka Univ.. 35. 1-5 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Takeuchi & M.Yokoyama: "PL-least area 2-orbifolds and its applications to 3-orbifolds"Kyushu J.Math.. (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] Y.Takeuchi & M.Yokoyama: "Waldhausen's classification theorem for 3-orbifolds"Kyushu J.Math.. 54・2. 371-401 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Yoshihide Okumura: "Lifting problem and its application to Riemann surfaces"Eighth International Conference on Complex Analysis. (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] 奥村善英: "リーマン面上の単純閉曲線が分割曲線になるための必要十分条件"京都大学数理解析研究所講究録. 1163. 28-41 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 奥村善英: "タイヒミュラー空間の角度変数とその応用"京都大学数理解析研究所講究録. (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] Hironori Kumura: "A note on the absence of eigenvalues on negatively curved manifold"Kyushu J.Math.. (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] Keiko Chiba: "Remarks on Suslin number of inverse limits"Reports of the Faculty of Science, Shizuoka University. 35. 1-5 (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] Yoshihiro Takeuchi &Misako Yokoyama: "PL-least area 2-orbifolds and its applications to 3-orbifolds"Kyushu J.Math.. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] Yoshihiro Takeuchi &Misako Yokoya: "Waldhausen's classification theorem for 3-orbifolds"Kyushu J.Math.. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] Yoshihiro Takeuchi &Misako Yokoyama: "The geometric realizations of the decompositions of 3-orbifold fundamental groups"Topology Appl.. 96. 129-153 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Keiko Chiba: "The strong paracompactness of δ-products"Scientiae Mathematicae. 2・3. 285-292 (1999)

    • Related Report
      1999 Annual Research Report

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Published: 2000-04-01   Modified: 2016-04-21  

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