Equivariant cohomological rigidity for four-dimensional Hamiltonian $S^1$-manifolds
Feb 10, 2025 3:00 - 4:00 pm
Altgeld Hall 243
- Sponsor
- Department of Mathematics
- Speaker
- Susan Tolman
- Views
- 74
- Originating Calendar
- Mathematics Seminar Series: Groups, Geometry, and Topology
Abstract: For manifolds equipped with group actions, we have the following natural question: To what extent does the equivariant cohomology determine the equivariant diffeotype? We resolve this question for Hamiltonian circle actions on compact, connected symplectic four-manifolds. They are equivariantly diffeomorphic if and only if their equivariant cohomology rings are isomorphic as algebras over the equivariant cohomology of a point.
In fact, we prove a stronger claim: each isomorphism between their equivariant cohomology rings is induced by an equivariant diffeomorphism.