The growth rate of Floer homology and symplectic zeta function

Details The growth rate of Floer homology and symplectic zeta function The growth rate of Floer homology and symplectic zeta function

2011-01-24

arxiv.org/abs/1101.4495v6

Mathematics

Symplectic Geometry

24 pages, Section 3.3 is added where a connection between symplectic Floer homology and geometry of 3-manifolds is established

Scientific paper

The main theme of this paper is to study for a symplectomorphism of a compact surface, the asymptotic invariant which is defined to be the growth rate of the sequence of the total dimensions of symplectic Floer homologies of the iterates of the symplectomorphism. We prove that the asymptotic invariant coincides with asymptotic Nielsen number and with asymptotic absolute Lefschetz number. We also show that the asymptotic invariant coincides with the largest dilatation of the pseudo-Anosov components of the symplectomorphism and its logarithm coincides with the topological entropy. This implies that symplectic zeta function has a positive radius of convergence.This also establishes a connection between Floer homology and geometry of 3-manifolds.

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