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We consider exact sequences and lower central series of surface braid groups and we explain how they can prove to be useful for obtaining representations for surface braid groups. In particular, using a completely algebraic framework, we describe the notion of extension of a representation introduced and studied recently by An and Ko and independently by Blanchet.
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 ess
Let M be a compact surface, either orientable or non-orientable. We study the lower central and derived series of the braid and pure braid groups of M in order to determine the values of n for which B_n(M) and P_n(M) are residually nilpotent or resid
Let $n, k geq 3$. In this paper, we analyse the quotient group $B_n/Gamma_k(P_n)$ of the Artin braid group $B_n$ by the subgroup $Gamma_k(P_n)$ belonging to the lower central series of the Artin pure braid group $P_n$. We prove that it is an almost-c
We introduce an algorithmic framework to investigate spherical and geodesic growth series of braid groups relatively to the Artins or Birman-Ko-Lees generators. We present our experimentations in the case of three and four strands and conjecture rati
A beautifully simple free generating set for the commutator subgroup of a free group was constructed by Tomaszewski. We give a new geometric proof of his theorem, and show how to give a similar free generating set for the commutator subgroup of a sur