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

Bellingeri, Paolo¹ ; Gervais, Sylvain²

¹Laboratoire de Mathématiques Nicolas Oresme, Université de Caen, CNRS UMR 6139, F-14000 Caen, France
²Laboratoire de Mathématique Jean Leray, Université de Nantes, CNRS UMR 6629, 2, rue de la Houssinière, BP 92208, F-44322 Cedex 3 Nantes, France

Algebraic and Geometric Topology, Tome 16 (2016) no. 1, pp. 547-568

Résumé

We prove that the nth 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 also prove some results on lower central series and augmentation ideals of p–almost direct products.

Détail

DOI : 10.2140/agt.2016.16.547

Classification : 20F14, 20F36, 57M05, 20D15
Keywords: pure braid groups, nonorientable surfaces, mod $p$ Torelli groups, residually $p$–finite, $p$–almost direct product, residually nilpotent, lower central series

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