Lower central series, surface braid groups, surjections and permutations

Abstract

Generalising previous results on classical braid groups by Artin and Lin, we determine the values of m, n $\in$ N for which there exists a surjection between the n-and m-string braid groups of an orientable surface without boundary. This result is essentially based on specific properties of their lower central series, and the proof is completely combinatorial. We provide similar but partial results in the case of orientable surfaces with boundary components and of non-orientable surfaces without boundary. We give also several results about the classification of different representations of surface braid groups in symmetric groups.

References in corpus (8)

• The lower central and derived series of the braid groups of the sphere and the punctured sphere
• Braids and Permutations
• Automorphisms of surface braid groups
• Homomorphisms between braid groups
• The lower central and derived series of the braid groups of the projective plane
• Abelian and metabelian quotients of surface braid groups
• The lower central and derived series of the braid groups of compact surfaces
• From braid groups to mapping class groups