We construct the vortex Floer homology group VHF (M, mu; H) for an aspherical Hamiltonian G-manifold (M, omega, mu) and a class of G-invariant Hamiltonian loops H-t, following a proposal of Cieliebak, Gaio, and Salamon (2000). This is a substitute for the ordinary Hamiltonian Floer homology of the symplectic quotient of M. The equation for connecting orbits is a perturbed symplectic vortex equation on the cylinder R x S-1. 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 Z.
展开▼
机译：根据Cieliebak，Gaio和Salamon的建议，我们为非球面哈密顿G流形（M，omega，mu）和一类G不变哈密顿环Ht构造了涡旋Floer同源群VHF（M，mu; H） （2000）。这是M辛商的普通哈密顿Floer同源性的替代。连接轨道的方程是圆柱R x S-1上的摄动辛涡旋方程。我们通过经典的扰动参数而不是虚拟技术来实现模空间的横向性，因此可以在Z上定义同源性。
展开▼
