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On $p$–almost direct
products and residual properties of pure braid groups of
nonorientable surfaces
Paolo Bellingeri and Sylvain Gervais |
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Algebraic & Geometric Topology 16 (2016) 547–568
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Abstract |
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We prove that the pure braid group of a nonorientable surface (closed or with boundary, but different from ) is residually –finite. Consequently, this group is residually nilpotent. The key ingredient in the closed case is the notion of –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 –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
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Mathematical Subject Classification 2010
Primary: 20F14, 20F36, 57M05
Secondary: 20D15
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References |
Publication
Received: 27 January 2015
Revised: 7 July 2015
Accepted: 8 July 2015
Published: 23 February 2016
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Authors |
| Paolo Bellingeri | |
| Laboratoire de Mathématiques Nicolas
Oresme Université de Caen CNRS UMR 6139 F-14000 Caen France |
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| 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 |
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| http://www.math.sciences.univ-nantes.fr/~gervais/ | |
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