37
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

The Natural Embedding of Positive Singular Artin Monoids

Pages 3329-3346 | Received 15 Apr 2005, Published online: 23 Nov 2006

REFERENCES

  • Antony , N. ( 2004 ). On the injectivity of the Vassiliev homomorphism of singular Artin monoids . Bull. Austral. Math. Soc. 70 : 401 – 422 .
  • Antony , N. ( 2005 ). On singular Artin monoids and contributions to Birman's conjecture . Comm. Algebra 33 : 4043 – 4056 . [CSA]
  • Artin , E. ( 1926 ). Theorie der Zöpfe . Abh. Math. Sem. Hamburg Univ. 4 : 47 – 72 . [CSA]
  • Baez , J. (1992). Link invariants of finite type and perturbation theory. Lett. Math. Phys. 26(1):43–51. [CSA] [CROSSREF]
  • Basset , G. ( 2000 ). Quasi-commuting extensions of groups . Comm. Algebra 28 : 5443 – 5454 . [CSA]
  • Bellingeri , P. ( 2004 ). Centralizers in surface braid groups . Comm. Algebra 32 : 4099 – 4115 . [CSA] [CROSSREF]
  • Birman , J. S. ( 1993 ). New points of view in knot theory . Bull. Amer. Math. Soc. (N.S.) 28 ( 2 ): 253 – 286 . [CSA]
  • Brieskorn , E. , Saito , K. ( 1972 ). Artin-Gruppen und Coxeter-Gruppen . Invent. Math. 17 : 245 – 271 . [CSA] [CROSSREF]
  • Corran , R. ( 2000 ). A normal form for a class of monoids including the singular braid monoid . J. Algebra 223 : 256 – 282 . [CSA] [CROSSREF]
  • Deligne , P. ( 1972 ). Les immeubles des groupes de tresses généralisés . Invent. Math. 17 : 273 – 302 . [CSA] [CROSSREF]
  • Daz-Cantos , J. , Gonzalez-Meneses , J. , Tornero , J. M. ( 2004 ). On the singular braid monoid of an orientable surface . Proc. Amer. Math. Soc. 132 : 2867 – 2873 . [CSA] [CROSSREF]
  • de la Harpe , P. ( 1990 ). An invitation to Coxeter groups . Group Theory from a Geometrical Viewpoint . (ICTP, Trieste, Italy, 1990), (World Scientific, 1991) , pp. 193 – 253 .
  • East , J. ( 2006 ). Birman's conjecture is true for I 2(P) . Knot Theory Ramifications 15 ( 2 ): 167 – 177 . [CSA] [CROSSREF]
  • Fenn , R. , Rolfsen , D. , Zhu , J. ( 1996 ). Centralizers in the braid group and the singular braid monoid . Enseign. Math. (2) 42 ( 1–2 ): 75 – 96 . [CSA]
  • Fenn , R. , Keyman , E. , Rourke , C. ( 1998 ). The singular braid monoid embeds in a group . J. Knot Theory Ramifications 7 ( 7 ): 881 – 892 . [CSA] [CROSSREF]
  • Garside , F. A. ( 1969 ). On the braid group and other groups . Quart. J. Math. Oxford Ser. 20 ( 2 ): 235 – 254 . [CSA]
  • Godelle , E. , Paris , L. ( 2005 ). On singular Artin monoids . Geometric Methods in Group Theory . Contemp. Math., 372, Amer. Math. Soc. , Providence , RI , pp. 43 – 57 .
  • González-Meneses , J. ( 2002 ). Presentations for the monoids of singular braids on closed surfaces . Comm. Algebra 30 ( 6 ): 2829 – 2836 . [CSA] [CROSSREF]
  • Humphreys , J. E. ( 1990 ). Reflection Groups and Coxeter Groups . Cambridge Studies in Advanced Mathematics , Vol. 29 , Cambridge , U.K. : Cambridge Univ. Press .
  • Járai , Jr , A. ( 1999 ). On the monoid of singular braids . Topology Appl. 96 : 109 – 119 . [CSA] [CROSSREF]
  • Keyman , E. ( 2001 ). A class of monoids embeddable in a group . Turkish J. Math. 25 : 299 – 305 . [CSA]
  • Paris , L. ( 2002 ). Artin monoids inject in their groups . Comment. Math. Helv. 77 : 609 – 637 . [CSA] [CROSSREF]
  • Paris , L. ( 2004 ). The proof of Birman's conjecture on singular braid monoids . Geom. Topol. 8 : 1281 – 1300 . [CSA] [CROSSREF]
  • Vassiliev , V. ( 1990 ). Cohomology of knot spaces . Theory of Singularities and its Applications . Arnold , V.I. Ed., Vol 1 . Amer. Math. Soc.
  • Zhu , J. ( 1997 ). On singular braids . J. Knot Theory Ramifications 6 : 427 – 440 . [CSA] [CROSSREF]
  • Communicated by V. Gould.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.