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Older papers
Special
groups with an elementary hierarchy are virtually free-by-Z.
With Dani Wise. Groups,
Geometry, and Dynamics 4:3,
597-603, 2010.
Weak
hyperbolicity
of cube
complexes and quasi-arboreal groups. J.
Topol. 7:2,
385-418, 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, 428-467, 2013.
The
simplicial boundary of a CAT(0) cube complex. Alg. Geom.
Topol. 13:3, 1299-1367, 2013. Corrigendum on Theorem 3.10 in the infinite-dimensional case; finite-dimensional case is unaffected (journal version).
Cocompactly
cubulated
crystallographic groups. J. Lond. Math. Soc. 90 (1): 140-166, 2014.
Cubulated
groups:
thickness,
relative hyperbolicity, and simplicial boundaries. With Jason Behrstock. Groups, Geometry, and Dynamics. (10:2) 649-707, 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: H-orbits are Hausdorff close to their convex hull in X. Nowadays, one would say "cubically convex-cocompact".
Cocompactly
cubulated
graph
manifolds.
With Piotr Przytycki. Isr. J. Math. 207 (1): 377-394, 2015.
Erratum correcting the proof of Lemma 4.7(2) (journal version).
Cubulating
hyperbolic free-by-cyclic groups: the irreducible case. With Dani
Wise. Duke Math. Jour. (165:9) 1753-1813, 2016.
Thickness,
relative
hyperbolicity, and randomness in Coxeter groups. With Jason Behrstock and Alessandro Sisto, appendix with Pierre-Emmanuel
Caprace. Alg. Geom. Topol. (17:2) 705-740, 2016.
Software associated with the above paper.
Residual finiteness
growths of virtually special groups. With Khalid Bou-Rabee
and Priyam Patel. Math. Zeit. 279 (1-2): 297-310, 2015.
Cubulating
hyperbolic free-by-cyclic groups: the general case. With Dani
Wise. Geom. Funct. Anal. 25:1, 134-179, 2015.
Hierarchically hyperbolic spaces I: curve complexes for cubical groups. With Jason Behrstock and Alessandro Sisto. Geom. Topol. (21:3) 1731-1804, 2017.
Quantifying separability in virtually special groups. With Priyam Patel. Pacific Jour. Math. (284:1) 103-120, 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 Falgas-Ravry, and Tim Susse. Int. Math. Res. Not. 2018:5, 1411-1441, 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) 257-338, 2019.
Asymptotic dimension and small-cancellation for hierarchically hyperbolic spaces and groups. With Jason Behrstock and Alessandro Sisto. Proc. Lond. Math. Soc. (114:5) 890-926, 2017.
Acylindrical hyperbolicity of cubical small-cancellation 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) 3659-3758, 2017.
Corrigendum fixing an error affecting the proofs of Theorem 7.1 and Theorem 9.15 (journal version).
Some point-set 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, 2016.
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