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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Vassiliev invariants for braids on surfaces


Authors: Juan González-Meneses and Luis Paris
Journal: Trans. Amer. Math. Soc. 356 (2004), 219-243
MSC (2000): Primary 20F36; Secondary 57M27, 57N05
Published electronically: August 25, 2003
MathSciNet review: 2020030
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Abstract: We show that Vassiliev invariants separate braids on a closed oriented surface, and we exhibit a universal Vassiliev invariant for these braids in terms of chord diagrams labeled by elements of the fundamental group of the surface.


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Additional Information

Juan González-Meneses
Affiliation: Departamento de Álgebra, Facultad de Matemáticas, Universidad de Sevilla, c/ Tarfia s/n, 41012 Sevilla, Spain
Email: meneses@us.es

Luis Paris
Affiliation: Université de Bourgogne, Laboratoire de Topologie, UMR 5584 du CNRS, B.P. 47870, 21078 - Dijon Cedex, France
Email: lparis@u-bourgogne.fr

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03116-7
PII: S 0002-9947(03)03116-7
Keywords: Braid, surface, Vassiliev invariant, finite type invariant
Received by editor(s): November 7, 2000
Received by editor(s) in revised form: May 20, 2002
Published electronically: August 25, 2003
Additional Notes: The first author was supported in part by DGESIC-PB97-0723, by BFM2001-3207 and by the European network TMR Sing. Eq. Diff. et Feuill
Article copyright: © Copyright 2003 American Mathematical Society