Related papers: Conjugacy problem for braid groups and Garside gro…

We introduce and investigate the ribbon groupoid associated with a Garside group. Under a technical hypothesis, we prove that this category is a Garside groupoid. We decompose this groupoid into a semi-direct product of two of its parabolic…

We study topological aspects of supersolvable abelian arrangements, toric arrangements in particular. The complement of such an arrangement sits atop a tower of fiber bundles, and we investigate the relationship between these bundles and…

We prove that every finitely-generated right-angled Artin group can be embedded into some Brin-Thompson group $nV$. It follows that many other groups can be embedded into some $nV$ (e.g., any finite extension of any of Haglund and Wise's…

We prove the Farrell-Jones fibered isomorphism conjecture for several classes of Artin groups of finite and affine types. As a consequence, we compute explicitly the surgery obstruction groups of the finite type pure Artin groups.

The submonoid of the $3$-strand braid group $\mathcal{B}_3$ generated by $\sigma_1$ and $\sigma_1 \sigma_2$ is known to yield an exotic Garside structure on $\mathcal{B}_3$. We introduce and study an infinite family $(M_n)_{n\geq 1}$ of…

We show that one can define and effectively compute Stallings graphs for quasi-convex subgroups of automatic groups (\textit{e.g.} hyperbolic groups or right-angled Artin groups). These Stallings graphs are finite labeled graphs, which are…

This thesis takes Brady's construction of $K(\pi,1)$s for the braid groups as a starting point. It is widely known that this construction can - with the right ingredients - be generalized to Artin groups of finite type. Results of Bessis as…

Inverse braid monoid describes a structure on braids where the number of strings is not fixed. So, some strings of initial $n$ may be deleted. In the paper we show that many properties and objects based on braid groups may be extended to…

We survey and compare various generalizations of braid groups for quivers with superpotential and focus on the cluster braid groups, which are introduced in a joint work with A.~King. Our motivations come from the study of cluster algebras,…

The maximum clique problem is a well known NP-Hard problem with applications in data mining, network analysis, information retrieval and many other areas related to the World Wide Web. There exist several algorithms for the problem with…

We show that the conjugacy problem is solvable in [finitely generated free]-by-cyclic groups, by using a result of O. Maslakova that one can algorithmically find generating sets for the fixed subgroups of free group automorphisms, and one…

Positive permutation braids on n strings, which are defined to be positive n-braids where each pair of strings crosses at most once, form the elementary but non-trivial building blocks in many studies of conjugacy in the braid groups. We…

We provide the first solution to the double coset problem (DCP) for a large class of natural subgroups of braid groups, namely for all parabolic subgroups which have a connected associated Coxeter graph. Update: We succeeded to solve the…

In their paper `A new algorithm for recognizing the unknot', in Geometry and Topology', 2 (1998) n. 9, 175-220, the first author and Michael Hirsch presented a then new algorithm for recognizing the unknot. The first part of the algorithm…

We characterize the double centralizer of all parabolic subgroups of the braid groups. We apply this result to provide a new and potentially more efficient solution to the subgroup conjugacy problem for parabolic subgroups. In the course of…

In this paper, we focus our attention on the connections between the braid group and the Nielsen fixed point theory. A new forcing relation between braids is introduced, and shown that it can be fulfilled by using Nielsen fixed point…

We design new deterministic and randomized algorithms for computational problems in free solvable groups. In particular, we prove that the word problem and the power problem can be solved in quasi-linear time and the conjugacy problem can…

We investigate the average-case complexity of decision problems for finitely generated groups, in particular the word and membership problems. Using our recent results on ``generic-case complexity'' we show that if a finitely generated…

In this work, we address a question posed by Dehornoy et al. in the book "Foundations of Garside Theory" that asks for a theory of groups of $\mathrm{I}_G$-type when $G$ is a Garside group. In this article, we introduce a broader notion…

We prove for the first time that, if a linear inverse problem exhibits a group symmetry structure, gradient-based optimizers can be designed to exploit this structure for faster convergence rates. This theoretical finding demonstrates the…