Finite, fiber- and orientation-preserving group actions on totally orientable Seifert manifolds

TL;DR

This paper characterizes finite groups acting fiber- and orientation-preservingly on orientable Seifert manifolds, providing a construction method and conditions under which these actions can be derived, along with their structural properties.

Contribution

It introduces a construction method for such group actions and refines the obstruction condition, detailing the structure of finite groups acting on Seifert manifolds.

Findings

Construction method for group actions on Seifert manifolds

Refined obstruction condition for actions

Structural description of acting finite groups

Abstract

In this paper we consider the finite groups that act fiber- and orientation-preservingly on closed, compact, and orientable Seifert manifolds that fiber over an orientable base space. We establish a method of constructing such group actions and then show that if an action satisfies a condition on the obstruction class of the Seifert manifold, it can be derived from the given construction. The obstruction condition is refined and the general structure of the finite groups that act via the construction is provided.