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arXiv · 1305.4536

Counting homotopy classes of mappings via Dijkgraaf-Witten invariants

Haimiao Chen
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Abstract

Suppose $Γ$ is a finite group acting freely on $S^{n}$ ($n\geqslant 3$ being odd) and $M$ is any closed oriented $n$-manifold. We show that, given an integer $k$, the set $°^{-1}(k)$ of based homotopy classes of mappings with degree $k$ is finite and its cardinality depends only on the congruence class of $k$ modulo $\#Γ$; moreover, $\#°^{-1}(k)$ can be expressed in terms of the Dijkgraaf-Witten invariants of $M$.

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Haimiao Chen. 2015-10-22. Counting homotopy classes of mappings via Dijkgraaf-Witten invariants. https://doi.org/10.1016/j.topol.2013.10.033

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