Equivariant cohomological rigidity of certain T–manifolds

Sarkar, Soumen; Song, Jongbaek

doi:10.2140/agt.2021.21.3601

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Equivariant cohomological rigidity of certain $T$–manifolds

Soumen Sarkar and Jongbaek Song

Algebraic & Geometric Topology 21 (2021) 3601–3622

DOI: 10.2140/agt.2021.21.3601

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

References

Publication

Received: 24 May 2020

Revised: 16 November 2020

Accepted: 20 December 2020

Published: 28 December 2021

Authors

Soumen Sarkar
Department of Mathematics Indian Institute of Technology Madras Madras India

Jongbaek Song
School of Mathematics KIAS Seoul South Korea

Volume 21, issue 7 (2021)