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arXiv · 1312.6923

Gauged Hamiltonian Floer homology I: definition of the Floer homology groups

Guangbo Xu
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Abstract

We construct the vortex Floer homology group $VHF (M,\mu;H)$ for an aspherical Hamiltonian $G$-manifold $(M, \omega)$ with moment map $\mu$ and a class of $G$-invariant Hamiltonian loop $H_t$, following the proposal of [3]. This is a substitute for the ordinary Hamiltonian Floer homology of the symplectic quotient of $M$. We achieve the transversality of the moduli space by the classical perturbation argument instead of the virtual technique, so the homology can be defined over ${\mathbb Z}$ or ${\mathbb Z}_2$.

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Guangbo Xu. 2013-12-25. Gauged Hamiltonian Floer homology I: definition of the Floer homology groups. https://arxiv.org/abs/1312.6923

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