Braids and crossed modules
Résumé
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