Comptes Rendus
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 ».

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.03.004

Hossein Abbaspour 1

1 Centre de mathématiques, École polytechnique, 91128 Palaiseau, France
@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},
}
TY  - JOUR
AU  - Hossein Abbaspour
TI  - The loop product for 3-manifolds
JO  - Comptes Rendus. Mathématique
PY  - 2004
SP  - 713
EP  - 718
VL  - 338
IS  - 9
PB  - Elsevier
DO  - 10.1016/j.crma.2004.03.004
LA  - en
ID  - CRMATH_2004__338_9_713_0
ER  - 
%0 Journal Article
%A Hossein Abbaspour
%T The loop product for 3-manifolds
%J Comptes Rendus. Mathématique
%D 2004
%P 713-718
%V 338
%N 9
%I Elsevier
%R 10.1016/j.crma.2004.03.004
%G en
%F CRMATH_2004__338_9_713_0
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] H. Abbaspour On string topology of 3-manifolds (Preprint) | arXiv

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

[3] W. Jaco; P. Shalen Seifert fibered spaces in 3-manifolds, Mem. Amer. Math. Soc., Volume 21 (1979), p. 220

[4] K. Johannson Homotopy Equivalence of 3-Manifolds with Boundaries, Lecture Notes in Math., vol. 761, Springer-Verlag, Berlin, 1979

[5] J. Milnor A unique decomposition theorem for 3-manifolds, Amer. J. Math., Volume 84 (1962), pp. 1-7

Cited by Sources:

Comments - Policy