Braids in trivial braid diagrams
Dehornoy, Patrick
HAL, hal-00000851 / Harvested from HAL
Text on HAL
We show that every trivial $3$-strand braid diagramcontains a disk, defined as a ribbon ending inopposed crossings. Under a convenient algebraicform, the result extends to every Artin--Titsgroup of dihedral type, but it fails toextend to braids with $4$~strands and more. Theproof uses a partition of the Cayley graph and acontinuity argument.
Publié le : 2004-07-05
Classification:  Garside monoid,  Cayley graph,  isotopy,  disk,  braid diagram,  MSC-class: 57M25, 20F36,  [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT] 
@article{hal-00000851,
     author = {Dehornoy, Patrick},
     title = {Braids in trivial braid diagrams},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00000851}
}

Dehornoy, Patrick. Braids in trivial braid diagrams. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00000851/