Charged Spaces

John R. Klein; John W. Peter

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arXiv · 1306.1753

Charged Spaces

John R. Klein·John W. Peter

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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 .

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John R. Klein, John W. Peter. 2013-06-07. Charged Spaces. https://arxiv.org/abs/1306.1753

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