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. 1975 Dec;72(12):4716–4717. doi: 10.1073/pnas.72.12.4716

A Bruhat decomposition for the loop space of a compact group: A new approach to results of Bott

Howard Garland *, M S Raghunathan †
PMCID: PMC388799  PMID: 16592292

Abstract

We give a new proof of Bott's result, that the loop space of a compact, simply connected, simple Lie group has a cellular decomposition of a certain type. In particular, one obtains the Poincaré polynomial for the loop space and Bott periodicity for the unitary group.

Keywords: Bott periodicity, loop spaces, Bruhat cells, Lie groups, cohomology

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Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Garland H. Dedekind's eta-function and the cohomology of infinite dimensional Lie algebras. Proc Natl Acad Sci U S A. 1975 Jul;72(7):2493–2495. doi: 10.1073/pnas.72.7.2493. [DOI] [PMC free article] [PubMed] [Google Scholar]

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