
Older papers
Special
groups with an elementary hierarchy are virtually freebyZ.
With Dani Wise. Groups,
Geometry, and Dynamics 4:3,
597603, 2010.
Weak
hyperbolicity
of cube
complexes and quasiarboreal groups. J.
Topol. 7:2,
385418, 2014.
On
embedding CAT(0)
cube complexes into products of trees via colouring their hyperplanes.
With Victor
Chepoi. J. Comb. Theor.
Ser. B
103:4, 428467, 2013.
The
simplicial boundary of a CAT(0) cube complex. Alg. Geom.
Topol. 13:3, 12991367, 2013. Corrigendum on Theorem 3.10 in the infinitedimensional case; finitedimensional case is unaffected (journal version).
Cocompactly
cubulated
crystallographic groups. J. Lond. Math. Soc. 90 (1): 140166, 2014.
Cubulated
groups:
thickness,
relative hyperbolicity, and simplicial boundaries. With Jason Behrstock. Groups, Geometry, and Dynamics. (10:2) 649707, 2016. Terminology clarification: the word "quasiconvex" is used in two ways in the paper, sometimes confusingly. In arguments not about group actions, it means "any two points in the subspace are joined by a quasigeodesic in the subspace". For a subgroup H of a group G acting geometrically on a cube complex X, "quasiconvex" is intended in the stronger, cubical sense: Horbits are Hausdorff close to their convex hull in X. Nowadays, one would say "cubically convexcocompact".
Cocompactly
cubulated
graph
manifolds.
With Piotr Przytycki. Isr. J. Math. 207 (1): 377394, 2015.
Erratum correcting the proof of Lemma 4.7(2) (journal version).
Cubulating
hyperbolic freebycyclic groups: the irreducible case. With Dani
Wise. Duke Math. Jour. (165:9) 17531813, 2016.
Thickness,
relative
hyperbolicity, and randomness in Coxeter groups. With Jason Behrstock and Alessandro Sisto, appendix with PierreEmmanuel
Caprace. Alg. Geom. Topol. (17:2) 705740, 2016.
Software associated with the above paper.
Residual finiteness
growths of virtually special groups. With Khalid BouRabee
and Priyam Patel. Math. Zeit. 279 (12): 297310, 2015.
Cubulating
hyperbolic freebycyclic groups: the general case. With Dani
Wise. Geom. Funct. Anal. 25:1, 134179, 2015.
Hierarchically hyperbolic spaces I: curve complexes for cubical groups. With Jason Behrstock and Alessandro Sisto. Geom. Topol. (21:3) 17311804, 2017.
Quantifying separability in virtually special groups. With Priyam Patel. Pacific Jour. Math. (284:1) 103120, 2016.
This is a slightly different proof of Theorem A. The main idea is the same, but the argument is modified in a way that avoids some technicalities. Not for publication, just a record for possible later use.
Global structural properties of random graphs. With Jason Behrstock, Victor FalgasRavry, and Tim Susse. Int. Math. Res. Not. 2018:5, 14111441, 2018.
Source code and data alluded to in the above paper.
Hierarchically hyperbolic spaces II: Combination theorems and the distance formula. With Jason Behrstock and Alessandro Sisto. Pacific J. Math. (299:2) 257338, 2019.
Asymptotic dimension and smallcancellation for hierarchically hyperbolic spaces and groups. With Jason Behrstock and Alessandro Sisto. Proc. Lond. Math. Soc. (114:5) 890926, 2017.
Acylindrical hyperbolicity of cubical smallcancellation groups. With Goulnara Arzhantseva. Alg. Geom. Topol. To appear, 2021.
Boundaries and automorphisms of hierarchically hyperbolic spaces. With Matthew Durham and Alessandro Sisto. Geom. Topol. (21:6) 36593758, 2017.
Corrigendum fixing an error affecting the proofs of Theorem 7.1 and Theorem 9.15 (journal version).
Some pointset topology comments, mainly explaining why the boundary of a proper HHS is metrisable. Not for publication since it's just giving details of ideas in the paper, but possibly helpful to someone reading Sections 2 and 3.
Cubulating mapping tori of polynomial growth free group automorphisms. With Dani Wise. Preprint, 2018.
This preprint is under repair (inductive step as written doesn't work). Will update here and on ArXiV when repairs are complete.
