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# Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2018: 0.71

Online
ISSN
1435-5337
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Volume 27, Issue 5

# Charged spaces

John R. Klein
/ John W. Peter
Published Online: 2013-11-23 | DOI: https://doi.org/10.1515/forum-2013-0096

## Abstract

Let C be a model category with an initial object $⌀$ and functorial factorizations. Let $S:C\to C$ be the suspension functor. An object X of C is said to be charged if it comes equipped with a map $S⌀\to X$. If Y is any object of C, then SY has a preferred charge, given by applying suspension to the map $⌀\to Y$. This motivates the question of whether a given charged object is a suspension up to a weak equivalence in a way that preserves charge structures. We study this question in the context of spaces over a given space, where we give a complete obstruction in a certain metastable range. As an application we show how this can be used to study when an embedding into a smooth manifold of the form N×I compresses to an embedding into N.

Keywords: Suspension; duality; fiberwise; embedding

MSC: 55R70; 55P40; 57R40; 57R19

Revised: 2013-09-11

Published Online: 2013-11-23

Published in Print: 2015-09-01

Citation Information: Forum Mathematicum, Volume 27, Issue 5, Pages 2661–2689, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741,

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