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

Spin^c Analysis for Group C^*-bundles on Manifolds and Study of Yamabe Invariants

Research Project

Project/Area Number 11640070
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

AKUTAGAWA Kazuo  Shizuoka University, Faculty of Science, Associated Professor, 理学部, 助教授 (80192920)

Co-Investigator(Kenkyū-buntansha) KUMURA Hironori  Shizuoka University, Faculty of Science, Full-Time Lecturer, 理学部, 講師 (30283336)
OKUMURA Yoshihide  Shizuoka University, Faculty of Science, Associated Professor, 理学部, 助教授 (90214080)
HIROKI Sato  Shizuoka University, Faculty of Science, Professor, 理学部, 教授 (40022222)
IZEKI Hiroyasu  Tohoku University, Graduate School of Science, Associated Professor, 大学院・理学研究科, 助教授 (90244409)
ONO Kaoru  Hokkaido University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (20204232)
Project Period (FY) 1999 – 2000
Project Status Completed (Fiscal Year 2000)
Budget Amount *help
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2000: ¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 1999: ¥1,700,000 (Direct Cost: ¥1,700,000)
KeywordsYamabe Invariant / Conformal Geometry / Differential Topology / Symplectic Geometry / Spin^c Geometry / Descrete Group / Cobordism / Manifolds of Negative Curvature / シンプレクティック多様体 / Seiberg-Witten理論 / 群C^*環 / ディラック作用素 / K理論
Research Abstract

We studied on Spin^c Analysis for Group C^*-bundles on Manifolds and Yamabe Invariants.
More precisely, we studied on the fundamentals of C^*-algebras and their K-theory. We also studied on the synthetic research of Yamabe invariants and Bordism theory with supergroups (i.e., supergroups, supergroup-structures on manifolds, supergroup C^*-bunbles and others). In particular, by using this bordism theory with supergroups, we obtained an obstruction to the positivity of relative Yamabe invariants. This result is written in the following paper :
Kazuo Akutagawa, An obstruction to the positivity of relative Yamabe invariants.
The head investigator, Kazuo Akutagawa also studied with professor Boris Botvinnik (University of Oregon) on Yamabe invariants from the algebraic topological viewpoint. Similar to the Homology theory, we defined a natural relative version of the Yamabe invariant, that is, the "relative Yamabe invariant", and we studied on it and the relation of the Yamabe invariant of a double manifold. This result is also written in the following papers :
Kazuo Akutagawa and Boris Botvinnik, Relative Yamabe invariant.
Kazuo Akutagawa and Boris Botvinnik, Manifolds of positive scalar curvature and conformal cobordism theory.

Report

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

    (26 results)

All Other

All Publications (26 results)

  • [Publications] Kazuo Akutagawa: "Notes on the relative Yamabe invariant""Differential Geometry", Josai Mathematical Monographs. 3. 105-113 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Reiko Aiyama and Kazuo Akutagawa: "The Dirichlet problem at infinity for harmonic map equations arising from constant mean curvature surfaces in the hyperbolic 3-space"Calc.Var.Partial Differential Equations. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Hiroki Sato: "One-parameter families of extreme discrete groups for Jorgensen's inequality"Contemporary Math.(The First Ahlfors-Bers Colloquium). 256. 271-287 (2000)

    • 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"The Eighth International Conference on Complex Analysis. (印刷中).

    • 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 manifolds"Kyusyu J.Math.. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Hiroyasu Izeki: "Quasiconformal stability of Kleinian groups and an embedding of a space of flat conformal structures"Conform.Geom.Dyn.. 4. 108-119 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Kazuo Akutagawa: "Notes on the relative Yamabe invariant""Differential Geometry", Josai Math.Monographs. 3. 105-113 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Reiko Aiyama and Kazuo Akutagawa: "The Dirichlet problem at infinity for harmonic map equations arising from constant mean curvature surfaces in the hyperbolic 3-space"Calc.Var.Partial Differential Equations. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Hiroki Sato: "One-parameter families of extreme discrete groups for Jorgensen's inequality"Contemporary Math.(The First Ahlfors-Bers Colloquium). 256. 271-287 (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: "Lifting problem and its application to Riemann surfaces"The 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] Hironori Kumura: "A note on the absence of eigenvalues on negatively curved manifolds"Kyusyu 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] Hiroshi Ohta and Kaoru Ono: "Simple singularities and topology of simplectically filling 4-manifolds"Comment.Math.Helvetici. 74. 575-590 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Hiroyasu Izeki: "Quasiconformal stability of Kleinian groups and an embedding of a space of flat conformal structures"Conform.Geom.Dyn.. 4. 108-119 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Kazuo Akutagawa: "Notes on the relative Yamabe invariant""Differential Geometry", Josai Mathematical Monographs. 3. 105-113 (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] Reiko Aiyama and Kazuo Akutagawa: "The Dirichlet problem at infinity for harmonic map equations arising from constant mean curvature surfaces in the hyperbolic 3-space"Calc.Var.Partial Differential Equations. (発表予定).

    • Related Report
      2000 Annual Research Report
  • [Publications] Hiroki Sato: "One-parameter families of extreme discrete groups for Jorgensen's inequality"Contemporary Math. (The First Ahlfors-Bers Colloquium). 256. 271-287 (2000)

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

    • Related Report
      2000 Annual Research Report
  • [Publications] Hironori Kumura: "A note on the absence of eigenvalues on negatively curved manifolds"Kyusyu J.Math.. (発表予定).

    • Related Report
      2000 Annual Research Report
  • [Publications] Hiroyasu Izeki: "Quasiconformal stability of Kleinian groups and an embedding of a space of flat conformal structures"Conform.Geom.Dyn.. 4. 108-119 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Kenji Fukaya,Y.-G.Oh,Hiroshi Ohta and Kaoru Ono: "Lagrangian intersection Floer homology,-anomally and obstruction-"(発表予定). 348

    • Related Report
      2000 Annual Research Report
  • [Publications] Reiko Aiyama and Kazuo Akutagawa: "Kenmotsu-Bryant type representation formulas for constant mean curvature surfaces in H^3(-c^2) and S^3_1(c^2)"Annals of Global Analysis and Geometry. 17. 49-75 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Kazuo Akutagawa: "Spin^c geometry,the Seiberg-Witten equations and Yamabe invariants of Kahler surfaces"Interdesciplinary Information Sciences.. 5-1. 55-72 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Reiko Aiyama and Kazuo Akutagawa: "Kenmotsu type representation formula for surfaces with prescribed mean curvature in the hyperbolic 3-space"Journal of the Mathematical Society of Japan.

    • Related Report
      1999 Annual Research Report
  • [Publications] Hiroki Sato: "One-parameter families of extreme discrete groups for J φrgensen's inequality"Contemporary Mathematics. (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] Kenji Fukaya and Kaoru Ono: "Arnold conjecture and Gromov-Witten invariant"Topology. 38. 933-1048 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Hiroshi Ohta and Kaoru Ono: "Simple singularities and topology of symplectically filling 4-manifolds"Commentarii Mathematici Helvetici. 74. 575-590 (1999)

    • Related Report
      1999 Annual Research Report

URL: 

Published: 1999-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi