Involutions of irreducible 3-manifolds containing two-sided projective planes
The author analyzes involutions (periodic homeomorphisms with period 2) on compact irreducible sufficiently large 3-manifolds containing 2-sided projective planes. Two involutions \(f\) and \(g\) of a manifold \(M\) are said to be strongly equivalent (relative to \(\partial M)\), if there exists a homeomorphism \(k\) (which restricts to the identity on \(\partial M)\), such that \(kfk^{- 1} = g\) and \(k\) is isotopic to the identity (relative to \(\partial M)\). First he classifies the strongly equivalent classes of involutions on \(P \times I\) and a certain more complicated manifold. Then he shows that two involutions which induce the same outer automorphism of the fundamental group are strongly equivalent in the complement of a regular neighborhood of an invariant set of projective planes, and he analyzes how they differ in this regular neighborhood. He also shows that under certain conditions, isotopic involutions are strongly equivalent.
compact irreducible sufficiently large 3- manifolds containing 2-sided projective planes
scientific article; zbMATH DE number 681629
scientific article