$\pi_1$ of symplectic automorphism groups and invertibles in quantum homology rings

TL;DR

This paper introduces a homomorphism linking the fundamental group of Hamiltonian automorphisms to invertible elements in quantum cohomology rings, expanding understanding of symplectic topology.

Contribution

It defines a new homomorphism applicable to a broader class of symplectic manifolds, with improved generality and novel examples and applications.

Findings

Established a homomorphism from fundamental groups to quantum cohomology invertibles.

Extended the framework to more general symplectic manifolds.

Provided new examples illustrating the theory.

Abstract

We define a homomorphism from (a certain extension of) the fundamental group of the Hamiltonian automorphism group of a symplectic manifold to the group of invertibles in its quantum cohomology ring. The manifold must satify a technical condition similar to weak monotonicity. This revised version has been entirely rewritten. It is more general and contains new examples and applications.