RESEARCH ANNOUNCEMENT: THE STRUCTURE OF GROUPS WITH A QUASICONVEX HIERARCHY

By Daniel T. Wise. 2009

384 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/399b6d834089933dd1e441dbfda0f3e26e62b8d7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Tits alternatives for graph products (2011, background): “The family of subgroups of right angled Artin groups is very rich and includes a lot of examples examples (see [1, 5, 10, 16, 17, 26, 37]).”
Weak hyperbolicity of cube complexes and quasi‐arboreal groups (2011, methodology): “13 can be proved using minimal-area disk diagrams and hexagon moves; see [36].”
The virtual Haken conjecture (2012, methodology): “However, we have decided to provide an alternative argument which gives a geometric perspective on the notion of height, and uses hyperbolic Dehn filling arguments from the literature instead of the small-cancellation theory developed in [45].”
Acylindrical hyperbolicity of groups acting on trees (2013, positive): “claim that many groups can be virtually embedded into right angled Artin groups (see [1,41,92] and references therein).”
Virtual cubulation of nonpositively curved graph manifolds (2011, background): “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]).”
Convex projective structures on nonhyperbolic three-manifolds (2015, methodology): “Finally, we briefly mention an application of the Cusp Covering Conjecture, proven by Wise (see [42] and [43, Corollary 16.”
Asymptotic dimension and small‐cancellation for hierarchically hyperbolic spaces and groups (2015, neutral): “Note that G need not be virtually special to satisfy the hypotheses of Corollary G (for example, the non-virtually special examples of Burger–Mozes and Wise [12, 32] act geometrically on the universal cover of the product of two finite graphs), so the corollary cannot be proved via cubical small-can”
The Thurston norm and twisted Alexander polynomials (2012, methodology): “The following theorem is also due to Przytycki-Wise.”
Contracting isometries of CAT(0) cube complexes and acylindrical hyperbolicity of diagram groups (2016, methodology): “For example, they were extensively used by Sageev in [Sag95] and by Wise in [Wis12].”