140 citations · 1.3k across the 89 of their papers we have counts for
69 papers · 1 filter
On symmetric and twisted-unitary modular units in group rings
Laurent Bartholdi, Iuliya Beloshapka, Roman Mikhailov
We study units in group rings of the Hantzsche-Wendt group. We construct a compatible system of non-trivial unitary units over for every , and ``alm…
Property (T) and Many Quotients
Laurent Bartholdi, Martin Kassabov
We prove that, for the free algebra over a sufficiently rich operad, a large subgroup of its group of tame automorphisms has Kazhdan's property (T). We deduce that there exists a g…
Growth of groups with linear Schreier graphs
Laurent Bartholdi, Volodymyr Nekrashevych, Tianyi Zheng
We introduce a new method of proving upper estimates of growth of finitely generated groups and constructing groups of intermediate growth using graphs of their actions. These esti…
Tree languages and branched groups
Laurent Bartholdi, Marialaura Noce
We study the portraits of isometries of rooted trees - the labelling of the tree, at each vertex, by the permutation of its descendants - in terms of languages. We characterize reg…
Monadic second-order logic and the domino problem on self-similar graphs
Laurent Bartholdi
We consider the domino problem on Schreier graphs of self-similar groups, and more generally their monadic second-order logic. On the one hand, we prove that if the group is bounde…
The Thue-Morse substitutions and self-similar groups and algebras
Laurent Bartholdi, José Manuel Rodríguez Caballero, Ahmed Tanbir
We introduce self-similar algebras and groups closely related to the Thue-Morse sequence, and begin their investigation by describing a character on them, the "spread" character.
The Thue-Morse shift, Baumslag-Solitar group, and biminimality
Laurent Bartholdi
Call a group action on a topological space \emph{biminimal} if for any points there exists a group element taking arbitrarily close to and whose inverse takes $y…
Groups with ALOGTIME-hard word problems and PSPACE-complete compressed word problems
Laurent Bartholdi, Michael Figelius, Markus Lohrey +1
We give lower bounds on the complexity of the word problem of certain non-solvable groups: for a large class of non-solvable infinite groups, including in particular free groups, G…
Right Angled Artin Groups and partial commutation, old and new
Laurent Bartholdi, Henrika Härer, Thomas Schick
We compute the -central and exponent- series of all right angled Artin groups, and compute the dimensions of their subquotients. We also describe their associated Lie algebra…
Self-similar products of groups
Laurent Bartholdi, Said N. Sidki
We address the problem of determining the class of self-similar groups, and in particular its closure under restricted direct products. We show that the group is…
Group and Lie algebra filtrations and homotopy groups of spheres
Laurent Bartholdi, Roman Mikhailov
We establish a bridge between homotopy groups of spheres and commutator calculus in groups, and solve in this manner the "dimension problem" by providing a converse to Sjogren's th…
An odd order group without the dimension property
Laurent Bartholdi, Roman Mikhailov
We construct a finitely presented group such that the th dimension quotient has an element of order ; this immediately leads to a…
Algorithmic aspects of branched coverings III/V. Erasing maps, orbispaces, and the Birman exact sequence
Laurent Bartholdi, Dzmitry Dudko
Let be a Thurston map and let be its mapping class biset: isotopy classes rel of maps obtained by pre- and…
The word and order problems for self-similar and automata groups
Laurent Bartholdi, Ivan Mitrofanov
We prove that the word problem is undecidable in functionally recursive groups, and that the order problem is undecidable in automata groups, even under the assumption that they ar…
Commutator width in the first Grigorchuk group
Laurent Bartholdi, Thorsten Groth, Igor Lysenok
Let be the first Grigorchuk group. We show that the commutator width of is : every element is a product of two commutators, and also of six conjugates of $a…
Decidability problems in automaton semigroups
Laurent Bartholdi
We consider decidability problems in self-similar semigroups, and in particular in semigroups of automatic transformations of . We describe algorithms answering the word probl…
Amenability of groups and -sets
Laurent Bartholdi
This text surveys classical and recent results in the field of amenability of groups, from a combinatorial standpoint. It has served as the support of courses at the University of…
Linear cellular automata, duality and sofic groups
Laurent Bartholdi
We produce for arbitrary non-amenable group and field a non-pre-injective, surjective linear cellular automaton. This answers positively Open Problem (OP-14) in Ceccherini-…
Algorithmic aspects of branched coverings II/V. Sphere bisets and their decompositions
Laurent Bartholdi, Dzmitry Dudko
We consider "Thurston maps": branched self-coverings of the sphere with ultimately periodic critical points, and prove that the Thurston equivalence problem between them (continuou…
The rational homology of the outer automorphism group of
Laurent Bartholdi
We compute the homology groups of the outer automorphism group of the free group of rank . We produce in this manner the first rational…
Algorithmic aspects of branched coverings I. Van Kampen's Theorem for bisets
Laurent Bartholdi, Dzmitry Dudko
We develop a general theory of "bisets": sets with two commuting group actions. They naturally encode topological correspondences. Just as van Kampen's theorem decomposes into a gr…
Growth of groups and wreath products
Laurent Bartholdi
These are introductory notes on word growth of groups, and include a gentle presentation of wreath products as well as recent results on construction of groups of with given growth…
On commutator length in free groups
Laurent Bartholdi, Danil Fialkovski, Sergei O. Ivanov
Let be a free group. We present for arbitrary a LogSpace (and thus polynomial time) algorithm that determines whether a given is a product of at most…
Distortion of imbeddings of groups of intermediate growth into metric spaces
Laurent Bartholdi, Anna G. Erschler
For every metric space in which there exists a sequence of finite groups of bounded-size generating set that does not embed coarsely, and for every unbounded, increasi…