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<p>A. Floer invented what is now called Floer theory in order to prove Arnold’s conjecture for fixed points of Hamiltonian diffeomorphisms. A symplectic diffeomorphism may not have fixed points, in general. There is a variant of Floer’s construction, i.e., Floer–Novikov theory, which we studied in previous works. Using Floer–Novikov homology associated with a certain covering space, we show a new existence result for a 1-periodic orbit of a 1-periodic family of symplectic vector fields on certain product symplectic manifolds with the prescribed Conley–Zehnder index, although Floer–Novikov homology vanishes in that degree.</p>

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A Symplectic Fixed Point Theorem and Floer–Novikov Theory in the Presence of an Infinite Fundamental Group

  • 期刊论文

  • 发表日期：

    2025年10月3日

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  • Hông Vân Lê,
  • Kaoru Ono

摘要

A. Floer invented what is now called Floer theory in order to prove Arnold’s conjecture for fixed points of Hamiltonian diffeomorphisms. A symplectic diffeomorphism may not have fixed points, in general. There is a variant of Floer’s construction, i.e., Floer–Novikov theory, which we studied in previous works. Using Floer–Novikov homology associated with a certain covering space, we show a new existence result for a 1-periodic orbit of a 1-periodic family of symplectic vector fields on certain product symplectic manifolds with the prescribed Conley–Zehnder index, although Floer–Novikov homology vanishes in that degree.