Counting homotopy classes of mappings via Dijkgraaf-Witten invariants

Abstract

Suppose $\Gamma$ is a finite group acting freely on $S^n$ ($n⩾3$ 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 $\#\Gamma$; moreover, $\#{°}^{-1}(k)$ can be expressed in terms of the Dijkgraaf-Witten invariants of $M$.

7 pages

References in corpus (1)

• The Dijkgraaf-Witten invariants of Seifert 3-manifolds with orientable bases

Cited by in corpus (1)

• The Dijkgraaf-Witten invariants of Seifert 3-manifolds with orientable bases