Borel cohomology and the relative Gorenstein condition for classifying spaces of compact Lie groups

2018/08/22 by J. P. C. Greenlees, Greenlees, J. P. C. · 1 citation
Mathematics · #13H10 #18E30 #20J06 #55N91 #55T20 #55U20 #55U25 #Advanced Algebra and Geometry #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1808.07342

openalex publication_date 2018/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a compact Lie group G we show that if the representing spectrum for Borel cohomology generates its category of modules if G is connected. For a closed subgroup H of G we consider the map C^*(BG)--->C^*(BH) and establish the sense in which it is relatively Gorenstein. Throughout, we pay careful attention to the importance of connectedness of the groups.

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