Poincare duality and Periodicity, II. James Periodicity
| dc.creator | Klein, John R. | |
| dc.creator | Richter, William | |
| dc.date | 2008-12-29 | |
| dc.date.accessioned | 2026-07-07T12:23:07Z | |
| dc.date.available | 2026-07-07T12:23:07Z | |
| dc.description | Let K be a connected finite complex. This paper studies the problem of whether one can attach a cell to some iterated suspension S^j K so that the resulting space satisfies Poincare duality. When this is possible, we say that S^j K is a spine. We introduce the notion of quadratic self duality and show that if K is quadratically self dual, then S^j K is a spine whenever j is a suitable power of two. The powers of two come from the James periodicity theorem. We briefly explain how our main results, considered up to bordism, give a new interpretation of the four-fold periodicity of the surgery obstruction groups. We therefore obtain a relationship between James periodicity and the four-fold periodicity in L-theory. | |
| dc.identifier | https://arxiv.org/abs/0812.4988 | |
| dc.identifier | http://arxiv.org/abs/0812.4988 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/213876 | |
| dc.subject | Algebraic Topology | |
| dc.subject | Geometric Topology | |
| dc.subject | 57P10, 57Q45 (Primary) 55Q25, 55P91 (Secondary) | |
| dc.title | Poincare duality and Periodicity, II. James Periodicity | |
| dc.type | text |