Yi Lin
Yi Lin

Ph.D. (2004) Cornell University

First Position
Dissertation
Advisor:
Research Area:
Abstract: Consider a Hamiltonian action of a compact Lie group on a symplectic manifold which has the strong Lefschetz property. We establish an equivariant version of the MerkulovGuillemin d\deltalemma, namely the d_G, \deltalemma, and an improved version of the KirwanGinzburg equivariant formality theorem, which says that every cohomology class has a canonical equivariant extension.
We then proceed to examine the equivariant cohomology of a compact strong Lefschetz Hamiltonian manifold (M, \omega) with generalized coefficients and establish a version of the d_G, \deltalemma for equivariant differential forms with generalized coefficients.
Consider a compact Hamiltonian circle manifold with the strong Lefschetz property. We constructed a family of 6 dimensional compact Hamiltonian S^1 manifold each of which satisfies the strong Lefschetz property itself but has a nonLefschetz symplectic quotient. As an aside we showed an interesting compact Hamiltonian circle manifold constructed by Karshon has the strong Lefschetz property.