Braids and Signatures
Bulletin de la Société Mathématique de France, Volume 133 (2005) no. 4, p. 541-579

A braid defines a link which has a signature. This defines a map from the braid group to the integers which is not a homomorphism. We relate the homomorphism defect of this map to Meyer cocycle and Maslov class. We give some information about the global geometry of the gordian metric space.

Une tresse définit un entrelacs qui possède une signature. Ceci définit une application du groupe des tresses vers les entiers qui n'est pas un homomorphisme. Nous relions le défaut d'homomorphisme de cette application au cocycle de Meyer et à la classe de Maslov. Nous donnons quelques informations sur la géométrie globale de l'espace métrique gordien.

DOI : https://doi.org/10.24033/bsmf.2496
Classification:  57M25
Keywords: knots, links, signature, Meyer cocycle, Maslov class
@article{BSMF_2005__133_4_541_0,
     author = {Gambaudo, Jean-Marc and Ghys, \'Etienne},
     title = {Braids and Signatures},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {133},
     number = {4},
     year = {2005},
     pages = {541-579},
     doi = {10.24033/bsmf.2496},
     zbl = {1103.57001},
     mrnumber = {2233695},
     language = {en},
     url = {http://www.numdam.org/item/BSMF_2005__133_4_541_0}
}
Gambaudo, Jean-Marc; Ghys, Étienne. Braids and Signatures. Bulletin de la Société Mathématique de France, Volume 133 (2005) no. 4, pp. 541-579. doi : 10.24033/bsmf.2496. http://www.numdam.org/item/BSMF_2005__133_4_541_0/

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