29 citations · 103 across the 19 of their papers we have counts for
6 papers · 1 filter
Finite index subgroups of mapping class groups
Luis Paris, Jon A Berrick, Volker Gebhardt
Let and , and let be the mapping class group of a surface of genus with boundary components. We prove that cont…
On the cycling operation in braid groups
Juan Gonzalez-Meneses, Volker Gebhardt
The cycling operation is a special kind of conjugation that can be applied to elements in Artin's braid groups, in order to reduce their length. It is a key ingredient of the usual…
Conjugacy in Garside Groups III: Periodic braids
Joan S. Birman, Volker Gebhardt, Juan Gonzalez-Meneses
An element in Artin's braid group B_n is said to be periodic if some power of it lies in the center of B_n. In this paper we prove that all previously known algorithms for solving…
Conjugacy in Garside groups II: Structure of the ultra summit set
Joan S. Birman, Volker Gebhardt, Juan Gonzalez-Meneses
This paper is the second in a series in which the authors study the conjugacy decision problem (CDP) and the conjugacy search problem (CSP) in Garside groups. The ultra summit set…
Conjugacy in Garside groups I: Cyclings, powers, and rigidity
Joan S. Birman, Volker Gebhardt, Juan Gonzalez-Meneses
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 having…
A New Approach to the Conjugacy Problem in Garside Groups
Volker Gebhardt
The cycling operation endows the super summit set of any element of a Garside group with the structure of a directed graph . We establish that the subset o…