The fixed subgroups of homeomorphisms of Seifert manifolds

Abstract

Let $M$ be a compact connected orientable Seifert manifold with hyperbolic orbifold $B_M$, and $f_{\pi }:{\pi }_1(M)\to {\pi }_1(M)$ be an automorphism induced by an orientation-reversing homeomorphism $f$ of $M$. We give a bound on the rank of the fixed subgroup of $f_{\pi }$, namely, $\rank\fix(f_π)<2\rank π_1(M)$, which is similar to the inequalities on surface groups and hyperbolic 3-manifold groups.

To appear in Acta Mathematica Sinica, English Series

References in corpus (1)

• The group fixed by a family of endomorphisms of a surface group

Cited by in corpus (1)

• Explicit bounds for fixed subgroups of endomorphisms of free products