Detecting mapping spaces

Detecting mapping spaces

We show if AA is a finite CW-complex such that algebraic theories detect mapping spaces out of AA, then AA has the homology type of a wedge of spheres of the same dimension. Furthermore, if AA is simply connected, then AA has the homotopy type of a wedge of spheres.

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Veröffentlicht in:Proceedings of the American Mathematical Society 2020-02, Vol.148 (6), p.2683-2693
1. Verfasser: Bittner, Alyson
Format: Artikel
Sprache:eng
Schlagworte:
Research article
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Zusammenfassung:We show if AA is a finite CW-complex such that algebraic theories detect mapping spaces out of AA, then AA has the homology type of a wedge of spheres of the same dimension. Furthermore, if AA is simply connected, then AA has the homotopy type of a wedge of spheres.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/14905