2019/09/30 by Soumen Sarkar, Jongbaek Song · 2 citations
Mathematics · #Advanced Combinatorial Mathematics #Algebra over a field #Algebraic structures and combinatorial models #Cohomology #Discrete mathematics #Equivariant cohomology #Equivariant map #Geometric and Algebraic Topology #Geometry #Homeomorphism (graph theory) #Manifold (fluid mechanics) #Mathematics #Pure mathematics #Rigidity (electromagnetism) #Torus #math.AT #math.SG #msc:53D10 #msc:55N91 #msc:57R91
paper · pdf · doi:10.2140/agt.2021.21.3601
published in Algebraic & Geometric Topology 21(7), 3601-3622 (Mathematical Sciences Publishers) · 17 pages, 1 figure
arxiv created 2020/12/21 · openalex publication_date 2021/12/28 · arxiv updated 2022/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We introduce the category of \it 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.