Braids and Signatures

Jean-Marc Gambaudo; Étienne Ghys

Bulletin de la Société Mathématique de France (2005)

  • Volume: 133, Issue: 4, page 541-579
  • ISSN: 0037-9484

Abstract

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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.

How to cite

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Gambaudo, Jean-Marc, and Ghys, Étienne. "Braids and Signatures." Bulletin de la Société Mathématique de France 133.4 (2005): 541-579. <http://eudml.org/doc/272312>.

@article{Gambaudo2005,
abstract = {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.},
author = {Gambaudo, Jean-Marc, Ghys, Étienne},
journal = {Bulletin de la Société Mathématique de France},
keywords = {knots; links; signature; Meyer cocycle; Maslov class},
language = {eng},
number = {4},
pages = {541-579},
publisher = {Société mathématique de France},
title = {Braids and Signatures},
url = {http://eudml.org/doc/272312},
volume = {133},
year = {2005},
}

TY - JOUR
AU - Gambaudo, Jean-Marc
AU - Ghys, Étienne
TI - Braids and Signatures
JO - Bulletin de la Société Mathématique de France
PY - 2005
PB - Société mathématique de France
VL - 133
IS - 4
SP - 541
EP - 579
AB - 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.
LA - eng
KW - knots; links; signature; Meyer cocycle; Maslov class
UR - http://eudml.org/doc/272312
ER -

References

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  11. [11] —, Knot theory and its applications, Birkhäuser, Boston, 1996, translated from the 1993 Japanese original by Bohdan Kurpita. MR1391727
  12. [12] D. Rolfsen – Knots and links, Math. Lecture Series, vol. 7, Publish or Perish, 1976. Zbl0339.55004MR515288
  13. [13] C. Squier – « The Burau representation is unitary », 90 (1984), p. 199–202. Zbl0542.20022MR727232
  14. [14] D. Sullivan – « On the intersection ring of compact three manifolds », 14 (1975), p. 275–277. Zbl0312.57003MR383415
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  16. [16] V. Turaev – « A cocycle of the symplectic first Chern class and Maslov indices », Funk. Anal. i Prilozhen. 18 (1984), p. 43–48, Russian; English translation: Funct. Anal. Appl., t.18 (1984), pp.35–39. Zbl0556.55012MR739088
  17. [17] C. Wall – « Non-additivity of the signature », 7 (1969), p. 269–274. Zbl0176.21501MR246311

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