Topology
The loop product for 3-manifolds
Comptes Rendus. Mathématique, Volume 338 (2004) no. 9, pp. 713-718.

Let M be a connected, closed, oriented and smooth manifold of dimension d. Let LM be the space of loops in M. Chas and Sullivan introduced the loop product, an associative product of degree −d on the homology of LM. In this Note we aim at identifying 3-manifolds with “non-trivial” loop products.

Pour M, une variété connexe, orientée et lisse de dimension d, soit LM l'espace des lacets libres de M. Chas et Sullivan ont défini un produit associatif de degré −d sur l'homologie de LM. Dans cette Note on vise à identifier les variétés de dimension 3 qui ont des produits de Chas–Sullivan « non-triviaux ».

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DOI: 10.1016/j.crma.2004.03.004
Abbaspour, Hossein 1

1 Centre de mathématiques, École polytechnique, 91128 Palaiseau, France
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Abbaspour, Hossein. The loop product for 3-manifolds. Comptes Rendus. Mathématique, Volume 338 (2004) no. 9, pp. 713-718. doi : 10.1016/j.crma.2004.03.004. http://www.numdam.org/articles/10.1016/j.crma.2004.03.004/

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[2] Chas, M.; Sullivan, D. String topology (Preprint) | arXiv

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