Exact sequences, lower central series and representations of surface braid groups

Abstract

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.

23 pages, 4 figures

References in corpus (2)

• The mapping class group of a genus two surface is linear
• On the Lie algebras of surface pure braid groups

Cited by in corpus (5)

• A survey of surface braid groups and the lower algebraic K-theory of their group rings
• On p-almost direct products and residual properties of pure braid groups of nonorientable surfaces
• Lower central series and split extensions
• Homological Construction of Quantum Representations of Mapping Class Groups
• Alexander invariants and cohomology jump loci in group extensions