Mixed 3-manifolds are virtually special

By Piotr Przytycki, Daniel T. Wise. 2012

138 citations recorded by the source corpus.

LetM be a compact oriented irreducible 3–manifold which is neither a graph manifold nor a hyperbolic manifold. We prove that π1M is virtually special.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/263943f1b921aa55da0876f79a48e7d55fdcdb31

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Graph manifolds with boundary are virtually special (2011, unknown): “Our theorem treats the complementary case, with an eye towards eventually analysing the case of manifolds with both hyperbolic and Seifert-fibred pieces [15].”
Convex projective structures on nonhyperbolic three-manifolds (2015, methodology): “Using cube complex techniques, Przytycki–Wise [34] showed that any mixed three-manifold, and therefore any manifold N as in Theorem 1.1, has linear fundamental group.”
The Thurston norm and twisted Alexander polynomials (2012, background): “The following theorem is also due to Przytycki–Wise (see [39]).”
Finiteness properties of cubulated groups (2012, background): “M. Here ♥∈ {r,∗,r∗}. There are two natural settings in which Theorem 8.13 applies: the ﬁrst is where X is a truncated ﬁnite volume hyperbolic 3–manifold; the second is where X is a “mixed” 3–manifold [PW]. In applications, verifying the hypotheses of Theorem 8.13 requires some care, but is primarily”
Virtual cubulation of nonpositively curved graph manifolds (2011, methodology): “We have also learned recently that Piotr Przytycki and Daniel Wise have an independent proof of the special cubulation for the bounded case using criteria of separability and double-coset separability of surface subgroups, ([PW1]).”