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

Guangbo Xu

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_…