Volume 16, issue 1 (2016)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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/