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Floer trajectories and stabilizing divisors

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Abstract

We incorporate pearly Floer trajectories into the tranversality scheme for pseudoholomorphic maps introduced by Cieliebak–Mohnke (J Symplectic Geom 5(3): 281–356, 2007). By choosing generic domain-dependent almost complex structures, we obtain zero- and one-dimensional moduli spaces with the structure of cell complexes with rational fundamental classes. Integrating over these moduli spaces gives a definition of Floer cohomology over Novikov rings via stabilizing divisors for rational Lagrangians that are fixed point sets of anti-symplectic involutions satisfying certain Maslov index conditions as well as Hamiltonian Floer cohomology of compact rational symplectic manifolds.

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Authors and Affiliations

  1. Department of Mathematics, Barnard College-Columbia University, MC 4433, 2990 Broadway, New York, NY, 10027, USA

    François Charest

  2. Mathematics-Hill Center, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ, 08854-8019, USA

    Chris Woodward

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  1. François Charest
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  2. Chris Woodward
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Correspondence to Chris Woodward.

Additional information

This work was partially supported by NSF Grant DMS 1207194 and FRQNT Grant B3 176181.

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Charest, F., Woodward, C. Floer trajectories and stabilizing divisors. J. Fixed Point Theory Appl. 19, 1165–1236 (2017). https://doi.org/10.1007/s11784-016-0379-8

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