Comptes Rendus
Differential Topology
Braids on surfaces and finite type invariants
Comptes Rendus. Mathématique, Volume 338 (2004) no. 2, pp. 157-162.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2003.11.014

Paolo Bellingeri 1; Louis Funar 2

1 Mathématiques, cc 051, Univ. Montpellier II, place Eugène Bataillon, 34095 Montpellier cedex 5, France
2 Institut Fourier, BP 74, Univ. Grenoble I, Mathématiques, 38402 Saint-Martin-d'Hères cedex, France
@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},
}
TY  - JOUR
AU  - Paolo Bellingeri
AU  - Louis Funar
TI  - Braids on surfaces and finite type invariants
JO  - Comptes Rendus. Mathématique
PY  - 2004
SP  - 157
EP  - 162
VL  - 338
IS  - 2
PB  - Elsevier
DO  - 10.1016/j.crma.2003.11.014
LA  - en
ID  - CRMATH_2004__338_2_157_0
ER  - 
%0 Journal Article
%A Paolo Bellingeri
%A Louis Funar
%T Braids on surfaces and finite type invariants
%J Comptes Rendus. Mathématique
%D 2004
%P 157-162
%V 338
%N 2
%I Elsevier
%R 10.1016/j.crma.2003.11.014
%G en
%F CRMATH_2004__338_2_157_0
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] J.E. Andersen; J. Mattes; N. Reshetikhin Quantization of the algebra of chord diagrams, Math. Proc. Cambridge Philos. Soc., Volume 124 (1998), pp. 451-467

[2] R. Bezrukavnikov Koszul DG-algebras arising from configuration spaces, Geom. Fumet. Anal., Volume 4 (1994), pp. 119-135

[3] P. Bellingeri On presentation of surface braid groups | arXiv

[4] J. Birman Braids, Links, and Mapping Class Groups, Ann. of Math. Stud., vol. 82, Princeton University Press, Princeton, NJ, 1973

[5] F.R. Cohen; T. Kohno; M.A. Xicotencatl Orbit configuration spaces associated to discrete subgroups of PSL(2,R) | arXiv

[6] E. Fadell; L. Neuwirth Configuration spaces, Math. Scand., Volume 10 (1962), pp. 111-118

[7] S. Garoufalidis; A. Kricker A rational noncommutative invariant of boundary links | arXiv

[8] J. González-Meneses New presentations of surface braid groups, J. Knot Theory Ramifications, Volume 10 (2001), pp. 431-451

[9] J. González-Meneses; L. Paris Vassiliev invariants for braids on surfaces, Trans. Amer. Math. Soc., Volume 356 (2004), pp. 219-243

[10] D.L. Goncalves; J. Guaschi On the structure of surface pure braid groups, J. Pure Appl. Algebra, Volume 182 (2003), pp. 33-64

[11] R. Hain Infinitesimal presentations of the Torelli groups, J. Amer. Math. Soc., Volume 10 (1997), pp. 597-651

[12] T. Kohno; T. Oda The lower central series of the pure braid group of an algebraic curve, Adv. Stud. Pure Math., Volume 12 (1987), pp. 201-219

[13] S. Lambropoulou 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] T.Q.T. Le; J. Murakami Representations of the category of tangles by Kontsevich's iterated integrals, Commun. Math. Phys., Volume 168 (1995), pp. 535-563

[15] H. Nakamura; N. Takao Galois rigidity of pro-l pure braid groups of algebraic curves, Trans. Amer. Math. Soc., Volume 350 (1998), pp. 1079-1102

[16] S. Papadima The universal finite-type invariant for braids, with integer coefficients, Topology Appl., Volume 118 (2002), pp. 169-185

[17] G.P. Scott Braid groups and the group of homeomorphisms of a surface, Math. Proc. Cambridge Philos. Soc., Volume 68 (1970), pp. 605-617

Cited by Sources:

Comments - Policy