Virtual cubulation of nonpositively curved graph manifolds

By Yi Liu. 2011

83 citations recorded by the source corpus.

In this paper, we show that an aspherical compact graph manifold is nonpositively curved if and only if its fundamental group virtually embeds into a right‐angled Artin group. As a consequence, nonpositively curved graph manifolds have linear fundamental groups.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/bdced60db4d30b7e147ffb484b43be99b0ae6c35

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In Applied Mathematics

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

The Thurston norm and twisted Alexander polynomials (2012, background): “lds with non-trivial JSJ decompositions, that are not virtually ﬁbered (see e.g. [Ne97, BS05]) and hence by Agol’s virtual ﬁbering theorem their fundamental groups are not virtually RFRS. In fact Liu [Liu11] (see also Przytycki and Wise [PW11]) showed that the fundamental group of an aspherical grap”
Tits alternatives for graph products (2011, background): “The family of subgroups of right angled Artin groups is very rich and includes many examples (see [4, 16, 15, 9, 25]).”
Hierarchically hyperbolic spaces II: Combination theorems and the distance formula (2015, background): “Indeed, when M is a nonpositively-curved graph manifold, π1M virtually acts freely, but not necessarily cocompactly, on a CAT(0) cube complex X , and the quotient is virtually special; this is a result of Liu [Liu11] which was also shown to hold in the case whereM has nonempty boundary by Przytycki ”
3-Manifold Groups (2012, methodology): “(Liu) Let N be an aspherical graph manifold.”