Charged Spaces
Algebraic Topology
2013-06-11 v2
Abstract
A charged space is a space equipped with two distinct base points. Such spaces arise as the unreduced suspension of an unbased space. More generally, one can work in the fiberwise setting over a fixed space B. A fiberwise charged space over B is a space X equipped with map to B and having two sections. One can ask whether or not a fiberwise charged space over B is a fiberwise suspension. We answer this question in a certain metastable range by producing a necessary and sufficient obstruction. As an application we show how this can be used to study when an embedding into a smooth manifold of the form N x I compresses to an embedding into N .
Keywords
Cite
@article{arxiv.1306.1753,
title = {Charged Spaces},
author = {John R. Klein and John W. Peter},
journal= {arXiv preprint arXiv:1306.1753},
year = {2013}
}