Geodesic
On the singular braid monoid
Algebra i analiz, Tome 21 (2009) no. 5, pp. 19-36.

Voir la notice de l'article provenant de la source Math-Net.Ru

Garside's results and the existence of the greedy normal form for braids are shown to be true for the singular braid monoid. An analog of the presentation of J. S. Birman, K. H. Ko, and S. J. Lee for the classical braid group is also obtained for this monoid. 
@article{AA_2009_21_5_a1,
     author = {V. V. Vershinin},
     title = {On the singular braid monoid},
     journal = {Algebra i analiz},
     pages = {19--36},
     publisher = {mathdoc},
     volume = {21},
     number = {5},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AA_2009_21_5_a1/}
}
TY  - JOUR
AU  - V. V. Vershinin
TI  - On the singular braid monoid
JO  - Algebra i analiz
PY  - 2009
SP  - 19
EP  - 36
VL  - 21
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AA_2009_21_5_a1/
LA  - ru
ID  - AA_2009_21_5_a1
ER  - 
%0 Journal Article
%A V. V. Vershinin
%T On the singular braid monoid
%J Algebra i analiz
%D 2009
%P 19-36
%V 21
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AA_2009_21_5_a1/
%G ru
%F AA_2009_21_5_a1
V. V. Vershinin. On the singular braid monoid. Algebra i analiz, Tome 21 (2009) no. 5, pp. 19-36. http://geodesic.mathdoc.fr/item/AA_2009_21_5_a1/

[1] Adyan S. I., “O fragmentakh slova $\Delta$ v gruppe kos”, Mat. zametki, 36:1 (1984), 25–34 | MR | Zbl

[2] Maltsev A. I., “O vklyuchenii assotsiativnykh sistem v gruppy. I”, Mat. sb., 6(48):2 (1939), 331–336 | MR | Zbl

[3] Maltsev A. I., “O vklyuchenii assotsiativnykh sistem v gruppy. II”, Mat. sb., 8(50):2 (1940), 251–264 | MR | Zbl

[4] Novikov P. S., “Ob algoritmicheskoi nerazreshimosti problemy tozhdestva slov v teorii grupp”, Tr. Mat. in-ta AN SSSR, 44, 1955, 3–143 | MR | Zbl

[5] Artin E., “Theorie der Zöpfe”, Abh. Math. Semin. Univ. Hamburg, 4 (1925), 47–72 | DOI | Zbl

[6] Baez J. C., “Link invariants of finite type and perturbation theory”, Lett. Math. Phys., 26:1 (1992), 43–51 | DOI | MR | Zbl

[7] Birman J. S., “New points of view in knot theory”, Bull. Amer. Math. Soc. (N.S.), 28:2 (1993), 253–287 | DOI | MR | Zbl

[8] Birman J. S., Ko K. H., Lee S. J., “A new approach to the word and conjugacy problems in the braid groups”, Adv. Math., 139:2 (1998), 322–353 | DOI | MR | Zbl

[9] Chaynikov V. V., “Garside structure for singular braid monoid in Birman, Ko, Lee generators”, Comm. Algebra, 34:6 (2006), 1981–1995 | DOI | MR | Zbl

[10] Corran R., “A normal form for a class of monoids including the singular braid monoids”, J. Algebra, 223:1 (2000), 256–282 | DOI | MR | Zbl

[11] Dasbach O. T., Gemein B., The word problem for the singular braid monoid, arxiv: math.GT/9809070

[12] El-Rifai E., Morton H. R., “Algorithms for positive braids”, Quart. J. Math. Oxford Ser. (2), 45:180 (1994), 479–497 | DOI | MR

[13] Epstein D. B. A., Cannon J. W., Holt D. F., Levy S. V. F., Paterson M. S., Thurston W. P., Word processing in groups, Jones and Bartlett Publishers, Boston, MA, 1992 | MR | Zbl

[14] Fenn R., Rolfsen D., Zhu J., “Centralisers in the braid group and singular braid monoid”, Enseign. Math. (2), 42:1–2 (1996), 75–96 | MR | Zbl

[15] Garside F. A., “The braid group and other groups”, Quart. J. Math. Oxford Ser. (2), 20 (1969), 235–254 | DOI | MR | Zbl

[16] Járai A. (Jr.), “On the monoid of singular braids”, Topology Appl., 96:2 (1999), 109–119 | DOI | MR

[17] Putcha M. S., “Conjugacy classes and nilpotent variety of a reductive monoid”, Canad. J. Math., 50:4 (1998), 829–844 | MR | Zbl