Morse-Bott Spectral Sequences and the Links of Singularities

Abstract

In this thesis, we construct spectral sequences converging to symplectic homology and equivariant symplectic homology groups. We use Morse-Bott type Hamiltonians and a natural action filtration. Those spectral sequences are called Morse-Bott spectral sequences. We apply the spectral sequences to a certain kind of symplectic manifolds with boundary, namely Milnor fibers whose boundaries are the links of singularities. In special cases, such as links of weighted homogeneous polynomials, they admit a nice symmetry along a periodic Reeb flow of a contact form. By means of those special symmetric feature, we present a systematic way of computing equivariant symplectic homology groups and its mean Euler characteristic. We obtain several applications of these machineries to exotic contact structures.