Diagrams and the second homotopy group
| dc.creator | Forester, Max | |
| dc.creator | Rourke, Colin | |
| dc.date | 2003-06-05 | |
| dc.date | 2004-10-18 | |
| dc.date.accessioned | 2026-07-07T06:26:50Z | |
| dc.date.available | 2026-07-07T06:26:50Z | |
| dc.description | We use Klyachko's methods [A funny property of sphere and equations over groups, Comm. in Alg. 21 (1993) 2555--2575] (see also Fenn-Rourke, L'Enseignment Math. 42 (1996) 49--74 and math.GR/9810184 and Cohen-Rourke, math.GR/0009101) to prove that, if a 1-cell and a 2-cell are added to a complex with torsion-free fundamental group, and with the 2-cell attached by an amenable t-shape, then pi_2 changes by extension of scalars. It then follows using a result of Bogley and Pride, Proc. Edinburgh Math. Soc. 35 (1992) 1--39, that the resulting fundamental group is also torsion free. We also prove that the normal closure of the attaching word contains no words of smaller complexity. | |
| dc.description | 18 pages 8 figures. Version 2: references added and deduction that the new fundamental group is also torsion free | |
| dc.identifier | https://arxiv.org/abs/math/0306088 | |
| dc.identifier | http://arxiv.org/abs/math/0306088 | |
| dc.identifier | Comm. Anal. Geom. 13 (2005) 801-820 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/97232 | |
| dc.subject | Algebraic Topology | |
| dc.subject | Group Theory | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M20, 57Q05; 20E22, 20F05 | |
| dc.title | Diagrams and the second homotopy group | |
| dc.type | text |