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

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.

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torus action, equivariant cohomology theory, cohomological rigidity, (quasi)toric manifold, contact toric manifold, moment–angle manifold, partial quotient
Mathematical Subject Classification
Primary: 55N91, 57R91
Received: 24 May 2020
Revised: 16 November 2020
Accepted: 20 December 2020
Published: 28 December 2021
Soumen Sarkar
Department of Mathematics
Indian Institute of Technology Madras
Jongbaek Song
School of Mathematics
South Korea