The realization space of an unstable coalgebra

Unstable coalgebras over the Steenrod algebra form a natural target category for singular homology with prime field coefficients. The realization problem asks whether an unstable coalgebra is isomorphic to the homology of a topological space. We study the moduli space of such realizations and give a...

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Bibliographic Details
Published in:arXiv.org 2017-08
Main Authors: Biedermann, Georg, Raptis, Georgios, Stelzer, Manfred
Format: Article
Language:English
Subjects:
Comparative studies
Homology
Online Access:Get full text
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Summary:Unstable coalgebras over the Steenrod algebra form a natural target category for singular homology with prime field coefficients. The realization problem asks whether an unstable coalgebra is isomorphic to the homology of a topological space. We study the moduli space of such realizations and give a description of this in terms of cohomological invariants of the unstable coalgebra. This is accomplished by a thorough comparative study of the homotopy theories of cosimplicial unstable coalgebras and of cosimplicial spaces.
ISSN:2331-8422