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Rational BV-algebra in string topology

Yves Félix、Jean‐Claude Thomas

2008Bulletin de la Société mathématique de FranceComputer Science被引 61开放获取

摘要

Let M be a 1-connected closed manifold of dimension m and LM be the space of free loops on M . M. Chas and D. Sullivan defined a structure of BValgebra on the singular homology of LM , H * (LM ; k). When the ring of coefficients is a field of characteristic zero, we prove that there exists a BV-algebra structure on the Hochschild cohomology HH * (C * (M ); C * (M )) which extends the canonical structure of Gerstenhaber algebra. We construct then an isomorphism of BV-algebras between HH * (C * (M ); C * (M )) and the shifted homology H * +m (LM ; k). We also prove that the Chas-Sullivan product and the BV-operator behave well with a Hodge decomposition of H * (LM ).

引用本文（GB/T 7714）

DOI：https://doi.org/10.24033/bsmf.2558