Geodesic
On the string topology coproduct for Lie groups
Homology, homotopy, and applications, Tome 24 (2022) no. 2, pp. 327-345.

Voir la notice de l'article provenant de la source International Press of Boston

The free loop space of a Lie group is homeomorphic to the product of the Lie group itself and its based loop space.We show that the coproduct on the homology of the free loop space that was introduced by Goresky and Hingston splits into the diagonal map on the group and a based coproduct on the homology of the based loop space. This result implies that the coproduct is trivial for even-dimensional Lie groups. Using results by Bott and Samelson, we show that the coproduct is trivial as well for a large family of simply connected Lie groups.
DOI : 10.4310/HHA.2022.v24.n2.a17
Classification : 55P50, 57T10
Keywords: string topology, Lie group 
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Maximilian Stegemeyer. On the string topology coproduct for Lie groups. Homology, homotopy, and applications, Tome 24 (2022) no. 2, pp. 327-345. doi : 10.4310/HHA.2022.v24.n2.a17. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2022.v24.n2.a17/

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