Comptes Rendus
no. 23-24
Topology
The Goldman bracket characterizes homeomorphisms
[Le crochet de Goldman caractérise les homéomorphismes]

Présenté par : the Editorial Board

Siddhartha Gadgil1
1 Department of Mathematics, Indian Institute of Science, Bangalore 560012, India
Comptes Rendus. Mathématique, Volume 349 (2011) no. 23-24, pp. 1269-1272.

Nous montrons quʼune équivalence dʼhomotopie entre des surfaces compactes, connexes, orientées et de bord non vide, est homotope à un homéomorphisme si et seulement si elle commute avec le crochet de Goldman.

We show that a homotopy equivalence between compact, connected, oriented surfaces with non-empty boundary is homotopic to a homeomorphism if and only if it commutes with the Goldman bracket.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.11.005

Siddhartha Gadgil 1

1 Department of Mathematics, Indian Institute of Science, Bangalore 560012, India 
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Siddhartha Gadgil. The Goldman bracket characterizes homeomorphisms. Comptes Rendus. Mathématique, Volume 349 (2011) no. 23-24, pp. 1269-1272. doi : 10.1016/j.crma.2011.11.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.11.005/

[1] A. Abbondandolo; M. Schwarz Floer homology of cotangent bundles and the loop product, Geom. Topol., Volume 14 (2010), pp. 1569-1722

[2] M. Chas Combinatorial Lie bialgebras of curves on surfaces, Topology, Volume 43 (2004), pp. 543-568

[3] M. Chas, D. Sullivan, String topology, Annals of Mathematics, in press, . | arXiv

[4] W.M. Goldman Invariant functions on Lie groups and Hamiltonian flows of surface group representations, Invent. Math., Volume 85 (1986) no. 2, pp. 263-302

[5] F. Waldhausen On irreducible 3-manifolds which are sufficiently large, Ann. of Math. (2), Volume 87 (1968), pp. 56-88

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