Topological group cohomology of Lie groups and Chern-Weil theory for compact symmetric spaces

Christoph Wockel

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arXiv · 1401.1037

Topological group cohomology of Lie groups and Chern-Weil theory for compact symmetric spaces

Christoph Wockel

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Abstract

In this paper we analyse the topological group cohomology of finite-dimensional Lie groups. We introduce a technique for computing it (as abelian groups) for torus coefficients by the naturally associated long exact sequence. The upshot in there is that certain morphisms in this long exact coefficient sequence can be accessed (at least for semi-simple Lie groups) very conveniently by the Chern-Weil homomorphism of the naturally associated compact dual symmetric space. Since the latter is very well-known, this gives the possibility to compute the topological group cohomology of the classical simple Lie groups. In addition, we establish a relation to characteristic classes of flat bundles.

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BibTeX RIS

Christoph Wockel. 2014-01-06. Topological group cohomology of Lie groups and Chern-Weil theory for compact symmetric spaces. https://arxiv.org/abs/1401.1037

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