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Brackets in the Free Loop Space Homology of Some Homogeneous Spaces

Volume 16, Number 1 (2013), 28 - 36

Brackets in the Free Loop Space Homology of Some Homogeneous Spaces

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Abstract

Let $X$ be a simply connected homogeneous space of which $ \pi_*(X) \otimes \Q $ is finite dimensional. We consider the homology of the free loop space $ \map(S^1, X)$ with the bracket defined by Chas and Sullivan. We show that the Lie algebra $ s\mathbb{H}_*(\map(S^1, X), \Q) $ is not nilpotent.