Volume 21, issue 7 (2021)

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Equivariant cohomological rigidity of certain $T$–manifolds

Soumen Sarkar and Jongbaek Song

Algebraic & Geometric Topology 21 (2021) 3601–3622
Abstract

We introduce the category of locally $k$–standard $T$–manifolds, which includes well-known classes of manifolds such as toric and quasitoric manifolds, good contact toric manifolds and moment–angle manifolds. They are smooth manifolds with well-behaved actions of tori. We study their topological properties, such as fundamental groups and equivariant cohomology algebras. Then we discuss when the torus equivariant cohomology algebra distinguishes them up to weakly equivariant homeomorphism.

Keywords
torus action, equivariant cohomology theory, cohomological rigidity, (quasi)toric manifold, contact toric manifold, moment–angle manifold, partial quotient
Mathematical Subject Classification
Primary: 55N91, 57R91