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Equivariant
cohomological rigidity of certain $T$–manifolds
Soumen Sarkar and Jongbaek Song |
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Algebraic & Geometric Topology 21 (2021) 3601–3622
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Abstract |
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We introduce the category of locally –standard –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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Keywords
torus action, equivariant cohomology theory, cohomological
rigidity, (quasi)toric manifold, contact toric manifold,
moment–angle manifold, partial quotient
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Mathematical Subject Classification
Primary: 55N91, 57R91
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References |
Publication
Received: 24 May 2020
Revised: 16 November 2020
Accepted: 20 December 2020
Published: 28 December 2021
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Authors |
| Soumen Sarkar | |
| Department of Mathematics Indian Institute of Technology Madras Madras India |
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| Jongbaek Song | |
| School of Mathematics KIAS Seoul South Korea |
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