149 citations · 595 across the 59 of their papers we have counts for
7 papers · 1 filter
Contracting elements and random walks
Alessandro Sisto
We define a new notion of contracting element of a group and we show that contracting elements coincide with hyperbolic elements in relatively hyperbolic groups, pseudo-Anosovs in…
Embedding universal covers of graph manifolds in products of trees
David Hume, Alessandro Sisto
We prove that the universal cover of any graph manifold quasi-isometrically embeds into a product of three trees. In particular we show that the Assouad-Nagata dimension of the uni…
Quasi-hyperbolic planes in relatively hyperbolic groups
John M. Mackay, Alessandro Sisto
We show that any group that is hyperbolic relative to virtually nilpotent subgroups, and does not admit peripheral splittings, contains a quasi-isometrically embedded copy of the h…
3-manifold groups have unique asymptotic cones
Alessandro Sisto
We describe the (minimal) tree-graded structure of asymptotic cones of non-geometric graph manifold groups, and as a consequence we show that all said asymptotic cones are bilipsch…
Iterated asymptotic cones
Lars Scheele, Alessandro Sisto
Iterated asymptotic cones have been used by Druţu and Sapir to construct a group with uncountably many pairwise non-homeomorphic asymptotic cones. In this paper we define a class o…
Exponential triples
Alessandro Sisto
Using ultrafilter techniques we show that in any partition of into 2 cells there is one cell containing infinitely many exponential triples, i.e. triples of the kind $…