Braids and crossed modules

Johannes Huebschmann (1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524

We describe Artin's braid group on a (fixed) finite number of strings as a crossed module over itself. In particular, we interpret the braid relations as crossed module structure relations.

Mots clés: Crossed module; identities among relations; geometric realization of a presention; pictures; Peiffer identities; Schur multiplicator; braid; braid group; augmented rack; automorphic structure; knot; link; tangle; quandle; knot group; link group; Hecke algebra; Wirtinger presentation; universal central extension; parallelohedron; permutahedron; operad

Domaines: Topologie algébrique [math.AT]; Théorie des groupes [math.GR]

Johannes Huebschmann. Braids and crossed modules. J. of Group Theory, 2012, 15, pp.57-83. ⟨10.1515/JGT.2011.095⟩. ⟨hal-00799525⟩