A natural, but slowly emerging program. In his PhD thesis prepared under the supervision of
Graham Higman and defended in 1965 [123], and in the article that followed [124], FA …

Publisher Summary Crossings are suggested as they are in a picture of a highway overpass
on a map. The identity braid has a canonical representation in which two strands never …

In this paper a relation between iterated cyclings and iterated powers of elements in a
Garside group is shown. This yields a characterization of elements in a Garside group …

In this paper we present a new key establishment protocol based on the decomposition
problem in non-commutative groups which is: given two elements $ w, w_1 $ of the platform …

Abstract These are Lecture Notes of a course given by the author at the French-Spanish
School Tresses in Pau, held in Pau (France) in October 2009. It is basically an introduction …

The nth root of a braid is unique up to conjugacy 1 Introduction Page 1 ISSN 1472-2739 (on-line)
1472-2747 (printed) 1103 Algebraic & Geometric Topology ATG Volume 3 (2003) 1103–1118 …

Conjugacy in Garside groups II: structure of the ultra summit set Page 1 Groups Geom. Dyn. 2
(2008), 13–61 Groups, Geometry, and Dynamics © European Mathematical Society Conjugacy …

We give a survey of the theory of surface braid groups and the lower algebraic K-theory of
their group rings. We recall several definitions and describe various properties of surface …

Motivated by cryptographic applications, we study subgroups of braid groups B n generated
by a small number of random elements of relatively small lengths compared to n. Our …

We give a new method to compute the centralizer of an element in Artin braid groups and,
more generally, in Garside groups. This method, together with the solution of the conjugacy …