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arXiv · 2412.14310

Equivariant cohomological rigidity for four-dimensional Hamiltonian $\mathbf{S^1}$-manifolds

Tara S. Holm·Liat Kessler·Susan Tolman
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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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Tara S. Holm, Liat Kessler, Susan Tolman. 2024-12-18. Equivariant cohomological rigidity for four-dimensional Hamiltonian $\mathbf{S^1}$-manifolds. https://arxiv.org/abs/2412.14310

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