14 citations · 93 across the 21 of their papers we have counts for
22 papers
The Twist Conjecture and the Isomorphism Problem for Coxeter groups
Elia Fioravanti
We prove Mühlherr's Twist Conjecture: any two angle-compatible Coxeter generating sets of a Coxeter group differ by a finite sequence of elementary twists and a conjugation. Combin…
Automorphism growth and group decompositions
Elia Fioravanti
Let be a finitely generated group with an automorphism , or an outer automorphism . Suppose that decomposes into simpler pieces on which…
--trees and accessibility over arc-stabilisers
Elia Fioravanti
Let be a minimal action on an --tree with finitely presented. Assuming that is accessible over the family of arc-stabilisers of , we gi…
Generators for automorphisms of special groups
Elia Fioravanti
Let be a (compact) special group in the sense of Haglund and Wise. We show that is finitely generated, and provide a virtual generating set consisting of Dehn tw…
On uniqueness of coarse median structures
Elia Fioravanti, Alessandro Sisto
We show that any product of bushy hyperbolic spaces has a unique coarse median structure, and that having a unique coarse median structure is a property closed under relative hyper…
Growth of automorphisms of virtually special groups
Elia Fioravanti
We study the speed of growth of iterates of outer automorphisms of virtually special groups, in the Haglund-Wise sense. We show that each automorphism grows either polynomially or…
Short positive loxodromics in graph products
Elia Fioravanti, Alice Kerr
We give a method for effectively generating generalised loxodromics in subgroups of graph products, using positive words. This has several consequences for the growth of subsets of…
Divisible cube complexes and finite-order automorphisms of RAAGs
Elia Fioravanti
We give a geometric characterisation of those groups that arise as fixed subgroups of finite-order untwisted automorphisms of right-angled Artin groups (RAAGs). They are precisely…
On the Čech cohomology of Morse boundaries
Elia Fioravanti, Annette Karrer, Alessandro Sisto +1
We consider cusped hyperbolic manifolds, and compute Čech cohomology groups of the Morse boundaries of their fundamental groups. In particular, we show that the reduced Čech co…
Coarse cubical rigidity
Elia Fioravanti, Ivan Levcovitz, Michah Sageev
We show that for many right-angled Artin and Coxeter groups, all cocompact cubulations coarsely look the same: they induce the same coarse median structure on the group. These are…
Connected components of Morse boundaries of graphs of groups
Elia Fioravanti, Annette Karrer
Let a finitely generated group split as a graph of groups. If edge groups are undistorted and do not contribute to the Morse boundary , we show that every connecte…
On automorphisms and splittings of special groups
Elia Fioravanti
We initiate the study of outer automorphism groups of special groups , in the Haglund-Wise sense. We show that is infinite if and only if splits over a co-abe…
Coarse-median preserving automorphisms
Elia Fioravanti
This paper has three main goals. First, we study fixed subgroups of automorphisms of right-angled Artin and Coxeter groups. If is an untwisted automorphism of a RAAG, or an arb…
Convex cores for actions on finite-rank median algebras
Elia Fioravanti
We show that every action of a finitely generated group on a finite-rank median algebra admits a nonempty "convex core", even when no metric or topology is given. We then use this…
Automorphisms of contact graphs of cube complexes
Elia Fioravanti
We show that, under weak assumptions, the automorphism group of a cube complex coincides with the automorphism group of Hagen's contact graph . T…
Deforming cubulations of hyperbolic groups
Elia Fioravanti, Mark Hagen
We describe a procedure to deform cubulations of hyperbolic groups by "bending hyperplanes". Our construction is inspired by related constructions like Thurston's Mickey Mouse exam…
Cross ratios on cube complexes and marked length-spectrum rigidity
Jonas Beyrer, Elia Fioravanti
We show that group actions on irreducible cube complexes with no free faces are uniquely determined by their length function. Actions are allowed to be non-…
Cross ratios and cubulations of hyperbolic groups
Jonas Beyrer, Elia Fioravanti
Many geometric structures associated to surface groups can be encoded in terms of invariant cross ratios on their circle at infinity; examples include points of Teichmüller space,…
cube complexes are determined by their boundary cross ratio
Jonas Beyrer, Elia Fioravanti, Merlin Incerti-Medici
We introduce a -valued cross ratio on Roller boundaries of cube complexes. We motivate its relevance by showing that every cross-ratio preserving bijecti…
Superrigidity of actions on finite rank median spaces
Elia Fioravanti
Finite rank median spaces are a simultaneous generalisation of finite dimensional cube complexes and real trees. If is an irreducible lattice in a product of ran…
The Tits alternative for finite rank median spaces
Elia Fioravanti
We prove a version of the Tits alternative for groups acting on complete, finite rank median spaces. This shows that group actions on finite rank median spaces are much more restri…
Roller boundaries for median spaces and algebras
Elia Fioravanti
We construct compactifications for median spaces with compact intervals, generalising Roller boundaries of cube complexes. Examples of median spaces with compact int…