Detecting Mapping Spaces
We show if $A$ is a finite CW-complex such that algebraic theories detect mapping spaces out of $A$, then $A$ has the homology type of a wedge of spheres of the same dimension. Furthermore, if $A$ is simply connected then $A$ has the homotopy type of a wedge of spheres.
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| Format: | Artikel |
| Sprache: | eng |
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| Zusammenfassung: | We show if $A$ is a finite CW-complex such that algebraic theories detect
mapping spaces out of $A$, then $A$ has the homology type of a wedge of spheres
of the same dimension. Furthermore, if $A$ is simply connected then $A$ has the
homotopy type of a wedge of spheres. |
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| DOI: | 10.48550/arxiv.1903.05668 |