We prove that there is no functorial universal finite type invariant for braids in Σ×I if the genus of Σ is positive.
Nous démontrons qu'il n'y a pas d'invariant universel fonctoriel de type fini pour les tresses dans Σ×I, lorsque Σ est une surface orientable de genre positif.
Accepted:
Published online:
Paolo Bellingeri 1; Louis Funar 2
@article{CRMATH_2004__338_2_157_0, author = {Paolo Bellingeri and Louis Funar}, title = {Braids on surfaces and finite type invariants}, journal = {Comptes Rendus. Math\'ematique}, pages = {157--162}, publisher = {Elsevier}, volume = {338}, number = {2}, year = {2004}, doi = {10.1016/j.crma.2003.11.014}, language = {en}, }
Paolo Bellingeri; Louis Funar. Braids on surfaces and finite type invariants. Comptes Rendus. Mathématique, Volume 338 (2004) no. 2, pp. 157-162. doi : 10.1016/j.crma.2003.11.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.11.014/
[1] Quantization of the algebra of chord diagrams, Math. Proc. Cambridge Philos. Soc., Volume 124 (1998), pp. 451-467
[2] Koszul DG-algebras arising from configuration spaces, Geom. Fumet. Anal., Volume 4 (1994), pp. 119-135
[3] On presentation of surface braid groups | arXiv
[4] Braids, Links, and Mapping Class Groups, Ann. of Math. Stud., vol. 82, Princeton University Press, Princeton, NJ, 1973
[5] Orbit configuration spaces associated to discrete subgroups of PSL(2,R) | arXiv
[6] Configuration spaces, Math. Scand., Volume 10 (1962), pp. 111-118
[7] A rational noncommutative invariant of boundary links | arXiv
[8] New presentations of surface braid groups, J. Knot Theory Ramifications, Volume 10 (2001), pp. 431-451
[9] Vassiliev invariants for braids on surfaces, Trans. Amer. Math. Soc., Volume 356 (2004), pp. 219-243
[10] On the structure of surface pure braid groups, J. Pure Appl. Algebra, Volume 182 (2003), pp. 33-64
[11] Infinitesimal presentations of the Torelli groups, J. Amer. Math. Soc., Volume 10 (1997), pp. 597-651
[12] The lower central series of the pure braid group of an algebraic curve, Adv. Stud. Pure Math., Volume 12 (1987), pp. 201-219
[13] Braid structures in knot complements, handlebodies and 3-manifolds, Knots in Hellas '98 (Delphi), Ser. Knots Everything, vol. 24, World Sci. Publishing, River Edge, NJ, 2000, pp. 274-289
[14] Representations of the category of tangles by Kontsevich's iterated integrals, Commun. Math. Phys., Volume 168 (1995), pp. 535-563
[15] Galois rigidity of pro-l pure braid groups of algebraic curves, Trans. Amer. Math. Soc., Volume 350 (1998), pp. 1079-1102
[16] The universal finite-type invariant for braids, with integer coefficients, Topology Appl., Volume 118 (2002), pp. 169-185
[17] Braid groups and the group of homeomorphisms of a surface, Math. Proc. Cambridge Philos. Soc., Volume 68 (1970), pp. 605-617
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