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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Hossein Abbaspour 1
@article{CRMATH_2004__338_9_713_0, author = {Hossein Abbaspour}, title = {The loop product for 3-manifolds}, journal = {Comptes Rendus. Math\'ematique}, pages = {713--718}, publisher = {Elsevier}, volume = {338}, number = {9}, year = {2004}, doi = {10.1016/j.crma.2004.03.004}, language = {en}, }
Hossein Abbaspour. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.03.004/
[1] On string topology of 3-manifolds (Preprint) | arXiv
[2] String topology (Preprint) | arXiv
[3] Seifert fibered spaces in 3-manifolds, Mem. Amer. Math. Soc., Volume 21 (1979), p. 220
[4] Homotopy Equivalence of 3-Manifolds with Boundaries, Lecture Notes in Math., vol. 761, Springer-Verlag, Berlin, 1979
[5] A unique decomposition theorem for 3-manifolds, Amer. J. Math., Volume 84 (1962), pp. 1-7
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