A JSJ splitting for triangulated open 3-manifolds

TL;DR

This paper extends the classical JSJ decomposition to a broader class of open 3-manifolds, providing a new criterion for their decomposition along embedded annuli and tori.

Contribution

It introduces a sufficient condition for open 3-manifolds to admit a JSJ-like splitting, generalizing previous results for closed manifolds.

Findings

Provides a new decomposition criterion for open 3-manifolds.

Generalizes the toric splitting to open manifolds.

Lays groundwork for further topological classification.

Abstract

We give a sufficient condition for an open 3-manifold to admit a decomposition along properly embedded open annuli and tori, generalizing the toric splitting of Jaco-Shalen and Johannson.