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Equivariant cohomological rigidity for four-dimensional Hamiltonian $S^1$-manifolds

Event Type
Seminar/Symposium
Sponsor
Department of Mathematics
Location
Altgeld Hall 243
Date
Feb 10, 2025   3:00 - 4:00 pm  
Speaker
Susan Tolman
Views
74
Originating Calendar
Groups, Geometry, and Topology Calendar

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.

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