Equivariant cohomology distinguishes toric manifolds
Algebraic Topology
2008-11-28 v1 Geometric Topology
Abstract
The equivariant cohomology of a space with a group action is not only a ring but also an algebra over the cohomology ring of the classifying space of the acting group. We prove that toric manifolds (i.e. compact smooth toric varieties) are isomorphic as varieties if and only if their equivariant cohomology algebras are weakly isomorphic. We also prove that quasitoric manifolds, which can be thought of as a topological counterpart to toric manifolds, are equivariantly homeomorphic if and only if their equivariant cohomology algebras are isomorphic.
Keywords
Cite
@article{arxiv.math/0703330,
title = {Equivariant cohomology distinguishes toric manifolds},
author = {Mikiya Masuda},
journal= {arXiv preprint arXiv:math/0703330},
year = {2008}
}