Involutions of irreducible 3-manifolds containing two-sided projective planes

Abstract

For a compact irreducible sufficiently large 3-manifold containing 2-sided projective planes, we consider the problem of when two involutions which induce the same outer automorphism on the fundamental group are strongly equivalent. We show that two such involutions are strongly equivalent in the complement of a regular neighborhood of an invariant set of projective planes, and analyze how they differ in this regular neighborhood. We show that under certain conditions, isotopic involutions are strongly equivalent.