2012/10/30 by Haggai Tene, Tene, Haggai
Mathematics · Medicine · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Ophthalmology and Eye Disorders
paper · pdf · doi:10.48550/arxiv.1210.7923
openalex publication_date 2012/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we give a geometric construction of the Borel equivariant (co)homology for spaces with a G-action, where G is a compact Lie group with the property that the adjoint representation is orientable. A nice feature of these constructions is that there are corresponding Poincaré dual (co)homology theories called backwards (co)homology. This gives rise to a third relative (co)homology theory which we call stratifold Tate (co)homology. These Tate groups agree with the original definition of Tate cohomology for finite groups given by Swan. All constructions in this paper are geometric and use stratifolds. One advantage of this description is that elements in these groups can be described concretely by representatives. We give some examples of that.