The cohomology rings of homogeneous spaces
| Autor: | Matthias O. Franz |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Classifying space
Pure mathematics 57T15 (Primary) 16E45 57T30 57T35 (Secondary) Homotopy 010102 general mathematics Gerstenhaber algebra Principal ideal domain Mathematics::Algebraic Topology 01 natural sciences Cohomology Mathematics::K-Theory and Homology 0103 physical sciences Homogeneous space FOS: Mathematics Torsion (algebra) Algebraic Topology (math.AT) Mathematics - Algebraic Topology 010307 mathematical physics Geometry and Topology Isomorphism 0101 mathematics Mathematics |
| Zdroj: | Journal of Topology. 14:1396-1447 |
| ISSN: | 1753-8424 1753-8416 |
| DOI: | 10.1112/topo.12213 |
| Popis: | Let $G$ be a compact connected Lie group and $K$ a closed connected subgroup. Assume that the order of any torsion element in the integral cohomology of $G$ and $K$ is invertible in a given principal ideal domain $k$. It is known that in this case the cohomology of the homogeneous space $G/K$ with coefficients in $k$ and the torsion product of $H^{*}(BK)$ and $k$ over $H^{*}(BG)$ are isomorphic as $k$-modules. We show that this isomorphism is multiplicative and natural in the pair $(G,K)$ provided that 2 is invertible in $k$. The proof uses homotopy Gerstenhaber algebras in an essential way. In particular, we show that the normalized singular cochains on the classifying space of a torus are formal as a homotopy Gerstenhaber algebra. 52 pages; new Sections 2.2 (Notation) and 13 (Examples), appendix expanded, minor changes |
| Databáze: | OpenAIRE |
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