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Proceedings of the London Mathematical Society, ISSN 1460-244X, 2019, Volume 118, Issue 6, pp. 1547 - 1591
We show that the smallest non‐abelian quotient of Aut(Fn) is PSLn(Z/2Z)=Ln(2), thus confirming a conjecture of Mecchia–Zimmermann. In the course of the proof... 
20E36 (secondary) | 20F65 (primary)
Journal Article
Journal of Topology, ISSN 1753-8416, 12/2017, Volume 10, Issue 4, pp. 970 - 994
For arbitrary positive integer n, we describe a large class of right‐angled Coxeter systems (W,S) for which the visual boundary ∂∞Σ(W,S) of the associated... 
20F65 (secondary) | 20F67 (primary) | 20F55
Journal Article
Boletín de la Sociedad Matemática Mexicana, ISSN 1405-213X, 10/2018, Volume 24, Issue 2, pp. 343 - 357
We construct two models for the classifying space for the family of infinite cyclic subgroups of the fundamental group of the Klein bottle. These examples do... 
20F65 | 55R35 | Mathematics, general | Mathematics
Journal Article
COMBINATORICA, ISSN 0209-9683, 11/2019, Volume 39, Issue 5, pp. 993 - 1019
We obtain an effective enumeration of the family of finitely generated groups admitting a faithful, properly discontinuous action on some 2-manifold contained... 
05C10 | 20F65 | MATHEMATICS | 20F05 | 05C25 | CONNECTIVITY
Journal Article
Journal of the London Mathematical Society, ISSN 0024-6107, 04/2019, Volume 99, Issue 2, pp. 583 - 608
Given a group G acting geometrically on a systolic complex X and a hyperbolic isometry h∈G, we study the associated action of h on the systolic boundary ∂X. We... 
20F65 | 20F69 (secondary) | 20F67 (primary) | MATHEMATICS | SPACES | Mathematics - Group Theory
Journal Article
Bulletin of the London Mathematical Society, ISSN 0024-6093, 02/2020, Volume 52, Issue 1, pp. 109 - 120
We prove that the simplicial complex whose simplices are the nonempty partial bases of Fn is homotopy equivalent to a wedge of (n−1)‐spheres. Moreover, we show... 
20F65 | 57M07 (primary) | 20E05 | 20E36 | MATHEMATICS | AUTOMORPHISM GROUP | HYPERBOLICITY | SUBGROUPS
Journal Article
Mathematische annalen, ISSN 1432-1807, 2014, Volume 362, Issue 3-4, pp. 1055 - 1105
We provide new examples of acylindrically hyperbolic groups arising from actions on simplicial trees. In particular, we consider amalgamated products and... 
20F65 | Primary 20F67 | 57M05 | 20E08 | Mathematics, general | Mathematics | 20E06 | Secondary 20E34 | MATHEMATICS | RESIDUAL PROPERTIES | PRODUCTS | BOUNDED COHOMOLOGY | II1 FACTORS | SQ-UNIVERSALITY | AUTOMORPHISMS | MANIFOLDS | SUBGROUPS | FREE ASSOCIATIVE ALGEBRA | STRUCTURAL THEORY | Algebra
Journal Article
Journal of Topology, ISSN 1753-8416, 09/2018, Volume 11, Issue 3, pp. 645 - 665
In this paper we provide a classification theorem for one‐dimensional boundaries of groups with isolated flats. Given a group Γ acting geometrically on a... 
20F65 | 20F67 (primary) | MATHEMATICS | DECOMPOSITIONS | CONTINUA
Journal Article
Proceedings of the London Mathematical Society, ISSN 0024-6115, 01/2019, Volume 118, Issue 1, pp. 143 - 190
Given non‐trivial finite groups A and B, not both of order 2, we prove that every finite simple group of sufficiently large rank is an image of the free... 
20P05 | 20F65 | 20D06 (primary) | 20E06 (secondary) | MATHEMATICS | MAXIMAL-SUBGROUPS | QUOTIENTS
Journal Article
Mathematische annalen, ISSN 1432-1807, 2011, Volume 352, Issue 2, pp. 339 - 356
We give a group theoretic characterization of geodesics with superlinear divergence in the Cayley graph of a right-angled Artin group A Γ with connected... 
20F65 | Mathematics, general | Mathematics | 20F36 | MATHEMATICS | BOUNDED COHOMOLOGY | LATTICES
Journal Article
Proceedings of the London Mathematical Society, ISSN 0024-6115, 05/2017, Volume 114, Issue 5, pp. 890 - 926
We prove that all hierarchically hyperbolic groups have finite asymptotic dimension. One application of this result is to obtain the sharpest known bound on... 
20F65 | 57M99 (primary) | MATHEMATICS | COMPLEX | GEOMETRY
Journal Article
Inventiones mathematicae, ISSN 0020-9910, 2/2019, Volume 215, Issue 2, pp. 713 - 740
We show that for every positive integer n there exists a simple group that is of type $$\mathrm {F}_{n-1}$$ F n - 1 but not of type $$\mathrm {F}_n$$ F n . For... 
Primary 20E32 | 20F65 | 20E08 | Mathematics, general | Mathematics | Secondary 57M07 | MATHEMATICS | THOMPSON GROUPS | SIGMA-INVARIANTS | ARITHMETIC GROUPS
Journal Article
Proceedings of the London Mathematical Society, ISSN 0024-6115, 01/2020, Volume 120, Issue 1, pp. 95 - 123
We prove that Artin groups from a class containing all large‐type Artin groups are systolic. This provides a concise yet precise description of their geometry.... 
20F65 | 20F36 | 20F67 (primary) | MATHEMATICS | BOUNDARIES | CONVEXITY | SUBGROUPS | FINITE-TYPE
Journal Article
Journal of the London Mathematical Society, ISSN 0024-6107, 12/2019, Volume 100, Issue 3, pp. 1065 - 1080
We obtain a sufficient and necessary condition for a finite group to act effectively on a closed flat manifold. Let G=En(R), EUn(R,Λ), SAut (Fn) or SOut (Fn).... 
20F65 | 22F05 | 57S17 (primary)
Journal Article
Mathematische Annalen, ISSN 0025-5831, 4/2016, Volume 364, Issue 3, pp. 937 - 982
We find new bounds on the conformal dimension of small cancellation groups. These are used to show that a random few relator group has conformal dimension $$2... 
20P05 | Primary 20F65 | Secondary 20F06 | Mathematics, general | Mathematics | 57M20 | 20F67
Journal Article
Mathematische annalen, ISSN 1432-1807, 2019, Volume 374, Issue 3-4, pp. 1311 - 1352
We introduce the notion of metrically systolic simplicial complexes. We study geometric and large-scale properties of such complexes and of groups acting on... 
20F65 | 20F10 | Mathematics, general | 20F06 | Mathematics | 20F36 | 20F67 | MATHEMATICS | AUTOMORPHISMS | SUBGROUPS | FINITE-TYPE | COMPLEXES | BRAID GROUP
Journal Article
Georgian Mathematical Journal, ISSN 1072-947X, 06/2019, Volume 26, Issue 2, pp. 303 - 309
Let be the geometric realization of a path-connected simplicial set , and let be the fundamental group. Given a subgroup , let be the set of cosets. Using the... 
20F65 | Covering map | necklical set | 55P35 | cubical set | 55U05 | 57M10
Journal Article
Inventiones mathematicae, ISSN 0020-9910, 2/2019, Volume 215, Issue 2, pp. 651 - 712
We prove the Farrell–Jones Conjecture for mapping class groups. The proof uses the Masur–Minsky theory of the large scale geometry of mapping class groups and... 
20F65 | Mathematics, general | Mathematics | 18F25 | CURVE COMPLEX | FOLIATIONS | INTERSECTION-NUMBERS | GEODESICS | MATHEMATICS | DIMENSION | K-THEORY | BOUNDARY | LATTICES | UNIFORM HYPERBOLICITY | GEOMETRY
Journal Article
Inventiones mathematicae, ISSN 0020-9910, 3/2019, Volume 215, Issue 3, pp. 819 - 862
We extend the notion of canonical measures to all (possibly non-compact) metric graphs. This will allow us to introduce a notion of “hyperbolic measures” on... 
20F65 | 57M60 | 05C12 | 05C63 | Mathematics, general | 14H30 | Mathematics | 14T05 | MATHEMATICS
Journal Article
Inventiones Mathematicae, ISSN 0020-9910, 07/2017, Volume 209, Issue 1, pp. 1 - 60
Let T be a locally finite tree all of whose vertices have valency at least 6. We classify, up to isomorphism, the closed subgroups of acting 2-transitively on... 
20F65 | 20E08 | 20E32 | 22D05 | 20E42 | 20B22 | MATHEMATICS
Journal Article
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