Fixed subgroups of automorphisms of hyperbolic 3-manifold groups

Abstract

For fixed subgroups $Fix(\varphi )$ of automorphisms $\varphi$ on hyperbolic 3-manifold groups ${\pi }_1(M)$, we observed that $\text{rk}(Fix(\varphi ))<2\text{rk}({\pi }_1(M))$ and the constant 2 in the inequality is sharp; we also classify all possible groups $Fix(\varphi )$.

16 pages, 3 figures