Juan González-Meneses

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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 rigid power, where 'rigid' means that the left normal form changes only in the obvious way under cycling and decycling. It is also shown that, given X in a Garside group, if(More)
This paper is the second in a series (the others are [2] and [3]) in which the authors study the conjugacy decision problem (CDP) and the conjugacy search problem (CSP) in Garside groups. The ultra summit set U SS(X) of an element X in a Garside group G is a finite set of elements in G, introduced in [14], which is a complete invariant of the conjugacy(More)
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 the conjugacy search problem in B n are exponential in the braid index n for the special case of periodic braids. We overcome this difficulty by putting to work several known(More)
This text consists of the introduction, table of contents, and bibliography of a long manuscript (703 pages) that is currently submitted for publication. This manuscript develops an extension of Garside's approach to braid groups and provides a unified treatment for the various algebraic structures that appear in this context. Introduction A natural, but(More)