The dual braid monoid

Bessis, David

doi:10.1016/j.ansens.2003.01.001

Bessis, David

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 36 (2003) no. 5, pp. 647-683.

MR Zbl | 8 citations dans Numdam

DOI : 10.1016/j.ansens.2003.01.001

@article{ASENS_2003_4_36_5_647_0,
     author = {Bessis, David},
     title = {The dual braid monoid},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {647--683},
     publisher = {Elsevier},
     volume = {Ser. 4, 36},
     number = {5},
     year = {2003},
     doi = {10.1016/j.ansens.2003.01.001},
     mrnumber = {2032983},
     zbl = {1064.20039},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.ansens.2003.01.001/}
}

TY  - JOUR
AU  - Bessis, David
TI  - The dual braid monoid
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 2003
SP  - 647
EP  - 683
VL  - 36
IS  - 5
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.ansens.2003.01.001/
DO  - 10.1016/j.ansens.2003.01.001
LA  - en
ID  - ASENS_2003_4_36_5_647_0
ER  -

%0 Journal Article
%A Bessis, David
%T The dual braid monoid
%J Annales scientifiques de l'École Normale Supérieure
%D 2003
%P 647-683
%V 36
%N 5
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.ansens.2003.01.001/
%R 10.1016/j.ansens.2003.01.001
%G en
%F ASENS_2003_4_36_5_647_0

Bessis, David. The dual braid monoid. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 36 (2003) no. 5, pp. 647-683. doi : 10.1016/j.ansens.2003.01.001. http://archive.numdam.org/articles/10.1016/j.ansens.2003.01.001/

Bibliographie
Cité par

[1] Bessis D., Zariski theorems and diagrams for braid groups, Invent. Math. 145 (2001) 487-507. | MR | Zbl

[2] Bessis D., Digne F., Michel J., Springer theory in braid groups and the Birman-Ko-Lee monoid, Pacific J. Math. 205 (2002) 287-310. | MR | Zbl

[3] Birman J., Ko K.H., Lee S.J., A new approach to the word and conjugacy problem in the braid groups, Adv. Math. 139 (2) (1998) 322-353. | MR | Zbl

[4] Bourbaki N., Groupes et algèbres de Lie, Hermann, 1968, chapitres IV, V et VI. | MR

[5] Brady T., A partial order on the symmetric group and new K(π,1)'s for the braid groups, Adv. Math. 161 (2001) 20-40. | Zbl

[6] Brady T., Watt C., A partial order on the orthogonal group, Comm. Algebra 30 (2002) 3749-3754. | MR | Zbl

[7] Brady T., Watt C., K(π,1)'s for Artin groups of finite type, Geom. Dedicata 94 (2002) 225-250. | Zbl

[8] Bremke K., Malle G., Reduced words and a length function for G(e,1,n), Indag. Math. (N.S.) 8 (4) (1997) 453-469. | MR | Zbl

[9] Brieskorn E., Die Fundamentalgruppe des Raumes der regulären Orbits einer endlichen komplexen Spiegelungsgruppe, Invent. Math. 12 (1971) 57-61. | MR | Zbl

[10] Brieskorn E., Saito K., Artin-Gruppen und Coxeter-Gruppen, Invent. Math. 17 (1972) 245-271. | MR | Zbl

[11] Broué M., Michel J., Sur certains éléments réguliers des groupes de Weyl et les variétés de Deligne-Lusztig associées, in: Proceedings de la Semaine de Luminy “Représentations des groupes réductifs finis, Birkhäuser, 1996, pp. 73-139. | Zbl

[12] Broué M., Malle G., Rouquier R., Complex reflection groups, braid groups, Hecke algebras, J. Reine Angew. Math. 500 (1998) 127-190. | MR | Zbl

[13] Carter R.W., Conjugacy classes in the Weyl groups, Compositio Math. 25 (1972) 1-52. | Numdam | MR | Zbl

[14] Charney R., Meier J., Whittlesey K., Bestvina's normal form complex and the homology of Garside groups, preprint, 2001.

[15] Corran R., A normal form for a class of monoids including the singular braid monoids, J. Algebra 223 (2000) 256-282. | MR | Zbl

[16] Dehornoy P., Groupes de Garside, Ann. Sci. Éc. Norm. Sup. (4) 35 (2002) 267-306. | Numdam | MR | Zbl

[17] Dehornoy P., Paris L., Gaussian groups and Garside groups, two generalizations of Artin groups, Proc. London Math. Soc. 79 (1999) 569-604. | MR | Zbl

[18] Deligne P., Les immeubles des groupes de tresses généralisés, Invent. Math. 17 (1972) 273-302. | MR | Zbl

[19] Deligne P., Action du groupe des tresses sur une catégorie, Invent. Math. 128 (1997) 159-175. | MR | Zbl

[20] Fomin S., Zelevinsky A., Y-systems and generalized associahedra, Ann. Math. (2003), submitted for publication. | MR | Zbl

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

[22] Gilbert N.D., Howie J., LOG groups and cyclically presented groups, J. Algebra 174 (1995) 118-131. | MR | Zbl

[23] Han J.W., Ko K.H., Positive presentations of the braid groups and the embedding problem, Math. Z. 240 (2002) 211-232. | MR | Zbl

[24] Michel J., A note on words in braid monoids, J. Algebra 215 (1999) 366-377. | MR | Zbl

[25] Picantin M., Explicit presentations for the dual braid monoids, C. R. Math. Acad. Sci. Paris 334 (10) (2002) 843-848. | MR | Zbl

[26] Reiner V., Non-crossing partitions for classical reflection groups, Discrete Math. 177 (1997) 195-222. | MR | Zbl

[27] Schönert M. et al. , GAP - Groups, Algorithms and Programming, Lehrstuhl D für Mathematik, RWTH Aachen, Germany, 1994.

[28] Sergiescu V., Graphes planaires et présentations des groupes de tresses, Math. Z. 214 (1993) 477-490. | MR | Zbl

[29] Solomon L., Invariants of finite reflection groups, Nagoya Math. J. 22 (1963) 57-64. | MR | Zbl

[30] Springer T.A., Regular elements of finite reflection groups, Invent. Math. 25 (1974) 159-198. | MR | Zbl

Cité par Sources :