On p-almost direct products and residual properties of pure braid groups of nonorientable surfaces

Paolo Bellingeri (1) , Sylvain Gervais (2)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 LMJL - Laboratoire de Mathématiques Jean Leray

We prove that the n th pure braid group of a nonorientable surface (closed or with boundary, but different from RP2) is residually 2-finite. Consequently, this group is residually nilpotent. The key ingredient in the closed case is the notion of p-almost direct product, which is a generalization of the notion of almost direct product. We prove therefore also some results on lower central series and augmentation ideals of p-almost direct products.

Mots clés: p-almost direct product; nonorientable surfaces; mod p Torelli group; braid groups; pure braid groups; lower central series; residually nilpotent; residually 2-finite

Domaines: Topologie géométrique [math.GT]; Théorie des groupes [math.GR]

Paolo Bellingeri, Sylvain Gervais. On p-almost direct products and residual properties of pure braid groups of nonorientable surfaces. Algebraic & Geometric Topology, 2016, 16 (1), pp.547-568. ⟨hal-01088951⟩