Degrees of Self-Mappings of Seifert Manifolds with Finite Fundamental Groups

Abstract

We calculate all degrees of selfmaps f : M $\rightarrow$ M of a Seifert manifold M with fundamental group of fi{}nite order N, provided that f induces an automorphism of $\pi_{1}$(M). The answer is given in terms of N, namely, the possible degrees $degf$ form the set $\left\{ k^{2}+\ell N\mid gcd\left(k,N\right)=1,k,\ell,\epsilon\mathbb{Z}\right\} $