Cocompact cubulations of mixed 3-manifolds

  • Joseph Tidmore

    University of Wisconsin-Milwaukee, USA


In this paper, we complete the classification of which compact 3-manifolds have a virtually compact special fundamental group by addressing the case of mixed 3-manifolds. A compact aspherical 3-manifold is mixed if its JSJ decomposition has at least one JSJ torus and at least one hyperbolic block. We show is virtually compact special if and only if is chargeless, i.e. each interior Seifert fibered block has a trivial Euler number relative to the fibers of adjacent blocks.

Cite this article

Joseph Tidmore, Cocompact cubulations of mixed 3-manifolds. Groups Geom. Dyn. 12 (2018), no. 4, pp. 1429–1460

DOI 10.4171/GGD/474