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Floer homology and Novikov rings

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The Floer Memorial Volume

Part of the book series: Progress in Mathematics ((PM,volume 133))

Abstract

We prove the Arnold conjecture for compact symplectic manifolds under the assumption that either the first Chern class of the tangent bundle vanishes over π2(M) or the minimal Chern number is at least half the dimension of the manifold. This includes the important class of Calabi-Yau manifolds. The key observation is that the Floer homology groups of the loop space form a module over Novikov’s ring of generalized Laurent series. The main difficulties to overcome are the presence of holomorphic spheres and the fact that the action functional is only well defined on the universal cover of the loop space with a possibly dense set of critical levels.

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Author information

Authors and Affiliations

  1. Departement Mathematik, ETH-Zentrum, CH-8092, Zürich, Germany

    Helmut Hofer

  2. Mathematics Institute, University of Warwick, CV4 7AL, Coventry, Great Britain

    Dietmar A. Salamon

Authors
  1. Helmut Hofer
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  2. Dietmar A. Salamon
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Editor information

Editors and Affiliations

  1. Dept. of Mathematics, ETH-Zentrum, 8092, Zürich, Switzerland

    Helmut Hofer  & Eduard Zehnder  & 

  2. Dept. of Mathematics, Harvard University, 02138, Cambridge, MA, USA

    Clifford H. Taubes

  3. Dept. of Mathematics, University of California, 94720, Berkeley, CA, USA

    Alan Weinstein

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© 1995 Birkhäuser Verlag

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Hofer, H., Salamon, D.A. (1995). Floer homology and Novikov rings. In: Hofer, H., Taubes, C.H., Weinstein, A., Zehnder, E. (eds) The Floer Memorial Volume. Progress in Mathematics, vol 133. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9217-9_20

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  • DOI: https://doi.org/10.1007/978-3-0348-9217-9_20

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9948-2

  • Online ISBN: 978-3-0348-9217-9

  • eBook Packages: Springer Book Archive

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