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2012 Homotopy normal maps
Matan Prezma
Algebr. Geom. Topol. 12(2): 1211-1238 (2012). DOI: 10.2140/agt.2012.12.1211


A group property made homotopical is a property of the corresponding classifying space. This train of thought can lead to a homotopical definition of normal maps between topological groups (or loop spaces).

In this paper we deal with such maps, called homotopy normal maps, which are topological group maps NG being “normal” in that they induce a compatible topological group structure on the homotopy quotient GN:=EN×NG. We develop the notion of homotopy normality and its basic properties and show it is invariant under homotopy monoidal endofunctors of topological spaces, eg localizations and completions. In the course of characterizing normality, we define a notion of a homotopy action of a loop space on a space phrased in terms of Segal’s 1–fold delooping machine. Homotopy actions are “flexible” in the sense they are invariant under homotopy monoidal functors, but can also rigidify to (strict) group actions.


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Matan Prezma. "Homotopy normal maps." Algebr. Geom. Topol. 12 (2) 1211 - 1238, 2012.


Received: 31 May 2011; Revised: 17 November 2011; Accepted: 29 January 2012; Published: 2012
First available in Project Euclid: 19 December 2017

zbMATH: 1277.18007
MathSciNet: MR2928911
Digital Object Identifier: 10.2140/agt.2012.12.1211

Primary: 18D10, 55P35
Secondary: 18G55, 55U10, 55U15, 55U30, 55U35

Rights: Copyright © 2012 Mathematical Sciences Publishers


Vol.12 • No. 2 • 2012
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