25 citations · 130 across the 19 of their papers we have counts for
19 papers
Free-by-cyclic groups are conjugacy separable
François Dahmani, Sam Hughes, Monika Kudlinska +1
We show that all finitely generated free-by-cyclic groups are conjugacy separable: if a finitely generated group surjects onto with free kernel, then for every pai…
The Conjugacy Problem for
François Dahmani, Stefano Francaviglia, Armando Martino +1
We present a solution to the Conjugacy Problem in the group of outer-automorphisms of , a free group of rank 3. We distinguish according to several computable invariants, such…
A fast algorithm for Stallings foldings over virtually free groups
Sam Cookson, Nicholas Touikan
We give a simple algorithm to solve the subgroup membership problem for virtually free groups. For a fixed virtually free group with a fixed generating set , the subgroup member…
Unipotent linear suspensions of free groups
François Dahmani, Nicholas Touikan
Motivated by the study of the conjugacy problem for outer automorphism of free groups, we develop the algorithmic theory of the free-by-cyclic group produced by unipotent linearly…
Reducing the conjugacy problem for relatively hyperbolic automorphisms to peripheral components
François Dahmani, Nicholas Touikan
We give a reduction of the conjugacy problem among outer automorphisms of free (and torsion-free hyperbolic) groups to specific algorithmic problems pertaining to mapping tori of p…
On the quasi-isometric rigidity of graphs of surface groups
Alexander Taam, Nicholas W. M. Touikan
Let be a word hyperbolic group with a cyclic JSJ decomposition that has only rigid vertex groups, which are all fundamental groups of closed surface groups. We show that any gr…
Panel collapse and its applications
Mark F. Hagen, Nicholas W. M. Touikan
We describe a procedure called panel collapse for replacing a CAT(0) cube complex by a "lower complexity" CAT(0) cube complex whenever contains a codimension-$2…
On geodesic ray bundles in hyperbolic groups
Nicholas Touikan
We construct a Cayley graph of a hyperbolic group such that there are elements and a point $γ\in \partial_\inftyΓ= \partial_\infty\mathbf{Cay}_S(Γ…
Magnus pairs in, and free conjugacy separability of, limit groups
Larsen Louder, Nicholas W. M. Touikan
There are limit groups having non-conjugate elements whose images are conjugate in every free quotient. Towers over free groups are freely conjugacy separable.
Multipass automata and group word problems
Tullio Ceccherini-Silberstein, Michel Coornaert, Francesca Fiorenzi +2
We introduce the notion of multipass automata as a generalization of pushdown automata and study the classes of languages accepted by such machines. The class of languages accepted…
On the one-endedness of graphs of groups
Nicholas Touikan
We give a technical result that implies a straightforward necessary and sufficient conditions for a graph of groups with virtually cyclic edge groups to be one ended. For arbitrary…
Deciding Isomorphy using Dehn fillings, the splitting case
François Dahmani, Nicholas Touikan
We solve Dehn's isomorphism problem for virtually torsion-free relatively hyperbolic groups with nilpotent parabolic subgroups. We do so by reducing the isomorphism problem to thre…
Strong accessibility for finitely presented groups
Larsen Louder, Nicholas Touikan
A hierarchy of a group is a rooted tree of groups obtained by iteratively passing to vertex groups of graphs of groups decompositions. We define a (relative) slender JSJ hierarchy…
Bulitko's Lemma for acylindrical splittings
Nicholas W. M. Touikan
We generalize Bulitko's Lemma to equations over (or homomorphisms into) groups that have -acylindrical splittings.
Detecting geometric splittings in finitely presented groups
Nicholas W. M. Touikan
We present an algorithm which given a presentation of a group without 2-torsion, a solution to the word problem with respect to this presentation, and an acylindricity constant…
The fully residually F quotients of F*<x,y>
Nicholas W. M. Touikan
We describe the fully residually F; or limit groups relative to F; (where F is a free group) that arise from systems of equations in two variables over F that have coefficients in…
A Fast Algorithm for Stallings' Folding Process
Nicholas Wembley Matheson Touikan
We show that for a fixed free group F and an arbitrary finitely generated subgroup H (as given above) we can perform the Stalling's folding process in time O(N log^*(N)), where N i…
Quadratic equations over free groups are NP-complete
O. Kharlampovich, I. G. Lysenok, A. G Myasnikov +1
We prove that the problems of deciding whether a quadratic equation over a free group has a solution is NP-complete.
The equation w(x,y)=u over free groups
Nicholas W M Touikan
Using the theory developed by Olga Kharlampovich, Alexei Miasnikov, and, independently, by Zlil Sela to describe the set of homomorphisms of a f.g. group G into a free group F, we…