Gauged Hamiltonian Floer homology. I: Definition of the Floer homology groups

DOI10.1090/TRAN/6643zbMATH Open1334.53093arXiv1312.6923OpenAlexW1781344431MaRDI QIDQ2787996

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Publication date: 7 March 2016

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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 $mathbbZ$ or ${mathbbZ}_2$.

Full work available at URL: https://arxiv.org/abs/1312.6923

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