On (pp-)almost direct products and residual properties of pure braid groups of surfaces.
Paolo Bellingeri (University of Caen)
Wednesday 22nd June, 2016 15:30-16:30 Maths 522
It is well known that pure braid groups are residually nilpotent, but all known proofs do not extend to pure braid groups on surfaces. However, in the case of surfaces with non empty boundary, the residual nilpotence of these groups can be verified constructing embeddings in some Torelli groups. The case of closed surface is more complicated: one possible solution implies the structure of (pp-)almost direct product of these groups. After a short survey on pure braid groups of surfaces, I will explain the notion of (pp)-almost direct product, its consequences on residual properties and I-adic filtrations and possible applications to finite type invariants for (surface) braids.