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2000 Fiscal Year Final Research Report Summary

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
KeywordsYamabe Invariant / Conformal Geometry / Differential Topology / Symplectic Geometry / Spin^c Geometry / Descrete Group / Cobordism / Manifolds of Negative Curvature
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.

  • Research Products

    (13 results)

All Other

All Publications (13 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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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

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Published: 2002-03-26  

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