On the peripheral subgroups of irreducible 3-manifold groups and acylindrical splittings

Abstract

We survey the problem of separation under conjugacy and malnormality of the abelian peripheral subgroups of an orientable, irreducible $3$-manifold $X$. We shall focus on the relation between this problem and the existence of acylindrical splittings of ${\pi }_1(X)$ as an amalgamated product or HNN-extension along the abelian subgroups corresponding to the JSJ-tori.

23 pages; corrected typos. Added a Proposition in section 4.1 (Proposition 4.5)

References in corpus (2)

• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Local topological rigidity of non-geometric $3$-manifolds

Cited by in corpus (1)

• Local topological rigidity of non-geometric $3$-manifolds