Repositorio de producción científica de la Universidad de Sevilla

Conjugacy in Garside groups II: Structure of the ultra summit set

Opened Access Conjugacy in Garside groups II: Structure of the ultra summit set

Citas

buscar en

Estadísticas
Icon
Exportar a
Autor: Birman, Joan S.
Gebhardt, Volker
González-Meneses López, Juan
Departamento: Universidad de Sevilla. Departamento de álgebra
Fecha: 2008
Publicado en: Groups, Geometry, and Dynamics, 2 (1), 13-61.
Tipo de documento: Artículo
Resumen: 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 USS(X) of an element X in a Garside group G is a finite set of elements in G, introduced by the second author, which is a complete invariant of the conjugacy class of X in G. A fundamental question, if one wishes to find bounds on the size of USS(X), is to understand its structure. In this paper we introduce two new operations on elements of USS(X), called `partial cycling' and `partial twisted decycling', and prove that if Y and Z belong to USS(X), then Y and Z are related by sequences of partial cyclings and partial twisted decyclings. These operations are a concrete way to understand the minimal simple elements which result from the convexity theorem in the mentioned paper by the second author. Using partial cycling and partial twisted decycling, we investigate the structure of a directed graph \Gamma_X w...
[Ver más]
Cita: Birman, J.S., Gebhardt, V. y González-Meneses López, J. (2008). Conjugacy in Garside groups II: Structure of the ultra summit set. Groups, Geometry, and Dynamics, 2 (1), 13-61.
Tamaño: 566.4Kb
Formato: PDF

URI: http://hdl.handle.net/11441/42278

DOI: http://dx.doi.org/10.4171/GGD/30

Mostrar el registro completo del ítem


Esta obra está bajo una Licencia Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 Internacional

Este registro aparece en las siguientes colecciones