On the singular braid monoid of an orientable surface
HTML articles powered by AMS MathViewer
- by Jerónimo Díaz-Cantos, Juan González-Meneses and José M. Tornero PDF
- Proc. Amer. Math. Soc. 132 (2004), 2867-2873 Request permission
Abstract:
In this paper we show that the singular braid monoid of an orientable surface can be embedded in a group. The proof is purely topological, making no use of the monoid presentation.References
- John C. Baez, Link invariants of finite type and perturbation theory, Lett. Math. Phys. 26 (1992), no. 1, 43–51. MR 1193625, DOI 10.1007/BF00420517
- Dror Bar-Natan, On the Vassiliev knot invariants, Topology 34 (1995), no. 2, 423–472. MR 1318886, DOI 10.1016/0040-9383(95)93237-2
- Gaëlle Basset, Quasi-commuting extensions of groups, Comm. Algebra 28 (2000), no. 11, 5443–5454. MR 1785510, DOI 10.1080/00927870008827165
- Joan S. Birman, Braids, links, and mapping class groups, Annals of Mathematics Studies, No. 82, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1974. MR 0375281
- Joan S. Birman, New points of view in knot theory, Bull. Amer. Math. Soc. (N.S.) 28 (1993), no. 2, 253–287. MR 1191478, DOI 10.1090/S0273-0979-1993-00389-6
- Roger Fenn, Ebru Keyman, and Colin Rourke, The singular braid monoid embeds in a group, J. Knot Theory Ramifications 7 (1998), no. 7, 881–892. MR 1654641, DOI 10.1142/S0218216598000462
- Juan González-Meneses, Presentations for the monoids of singular braids on closed surfaces, Comm. Algebra 30 (2002), no. 6, 2829–2836. MR 1908240, DOI 10.1081/AGB-120003991
Additional Information
- Jerónimo Díaz-Cantos
- Affiliation: Departamento de Álgebra, Universidad de Sevilla, Apdo. 1160, 41080 Sevilla, Spain
- Juan González-Meneses
- Affiliation: Departamento de Matemática Aplicada I, E.T.S. de Arquitectura, Universidad de Sevilla, Avda. Reina Mercedes, 41013 Sevilla, Spain
- Address at time of publication: Departamento de Álgebra, Universidad de Sevilla, Apdo. 1160, 41080 Sevilla, Spain
- Email: meneses@us.es
- José M. Tornero
- Affiliation: Departamento de Álgebra, Universidad de Sevilla, Apdo. 1160, 41080 Sevilla, Spain
- Email: tornero@us.es
- Received by editor(s): February 21, 2003
- Received by editor(s) in revised form: April 1, 2003
- Published electronically: May 20, 2004
- Additional Notes: The second author was supported by BFM 2001–3207 and FQM 218.
The third author was supported by BFM 2001–3207 and FQM 218. - Communicated by: Ronald A. Fintushel
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 2867-2873
- MSC (2000): Primary 20F36; Secondary 20F38
- DOI: https://doi.org/10.1090/S0002-9939-04-07307-1
- MathSciNet review: 2063105