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

H Garland; M S Raghunathan

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

Proc Natl Acad Sci U S A. 1975 Dec;72(12):4716-7. doi: 10.1073/pnas.72.12.4716.

Authors

H Garland¹, M S Raghunathan

Affiliation

¹ Yale University, New Haven, Connecticut 06520.

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.