Volume 16, issue 1 (2016)

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

Paolo Bellingeri and Sylvain Gervais

Algebraic & Geometric Topology 16 (2016) 547–568
Abstract

We prove that the nth pure braid group of a nonorientable surface (closed or with boundary, but different from 2) 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.

Keywords
pure braid groups, nonorientable surfaces, mod $p$ Torelli groups, residually $p$–finite, $p$–almost direct product, residually nilpotent, lower central series
Mathematical Subject Classification 2010
Primary: 20F14, 20F36, 57M05
Secondary: 20D15
References
Publication
Received: 27 January 2015
Revised: 7 July 2015
Accepted: 8 July 2015
Published: 23 February 2016
Authors
Paolo Bellingeri
Laboratoire de Mathématiques Nicolas Oresme
Université de Caen
CNRS UMR 6139
F-14000 Caen
France
http://www.math.unicaen.fr/~bellinge/
Sylvain Gervais
Laboratoire de Mathématique Jean Leray
Université de Nantes
CNRS UMR 6629
2, rue de la Houssinière
BP 92208
F-44322 Cedex 3 Nantes
France
http://www.math.sciences.univ-nantes.fr/~gervais/