Poincare duality and Periodicity
Algebraic Topology
2014-10-01 v4 Geometric Topology
Abstract
We construct periodic families of Poincare complexes, partially solving a question of Hodgson that was posed in the proceedings of the 1982 Northwestern homotopy theory conference. We also construct infinite families of Poincare complexes whose top cell falls off after one suspension but which fail to embed in a sphere of codimension one. We give a homotopy theoretic description of the four-fold periodicity in knot cobordism.
Cite
@article{arxiv.0707.1353,
title = {Poincare duality and Periodicity},
author = {John R. Klein and William Richter},
journal= {arXiv preprint arXiv:0707.1353},
year = {2014}
}
Comments
A significant revision. In this version we produce infinite families of examples of Poincare complexes whose top cell falls off after one suspension, but which do not embed in codimension one. We also rewrote the knot periodicity section in terms of Seifert surfaces rather than knot complements