Algorithmic Problems in the Braid Group: Theory and Applications - Couverture souple

Feder, Elie

 
9783639138986: Algorithmic Problems in the Braid Group: Theory and Applications
Couverture souple
ISBN 10 : 3639138988 ISBN 13 : 9783639138986
Editeur : VDM Verlag Dr. Müller, 2009

Synopsis

The study of braid groups and their applications is a field which has attracted the interest of mathematicians and computer scientists alike. We begin with a review of the notion of a braid group. We then discuss known solutions to decision problems in braid groups. We then prove new results in braid group algorithmics. We offer a quick solution to the generalized word problem in braid groups, in the special case of cyclic subgroups. We illustrate this solution using a multitape Turing machine. We then turn to a discussion of decision problems in cyclic amalgamations of groups and solve the word problem for the cyclic amalgamation of two braid groups. We then turn to a more general study of the conjugacy problem in cyclic amalgamations. We revise and prove some theorems of Lipschutz and show their application to cyclic amalgamations of braid groups. We generalize this application to prove a new theorem regarding the conjugacy problem in cyclic amalgamations. We then discuss some application of braid groups, culminating in a section devoted to the discussion of braid group cryptography.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

The study of braid groups and their applications is a field which has attracted the interest of mathematicians and computer scientists alike. We begin with a review of the notion of a braid group. We then discuss known solutions to decision problems in braid groups. We then prove new results in braid group algorithmics. We offer a quick solution to the generalized word problem in braid groups, in the special case of cyclic subgroups. We illustrate this solution using a multitape Turing machine. We then turn to a discussion of decision problems in cyclic amalgamations of groups and solve the word problem for the cyclic amalgamation of two braid groups. We then turn to a more general study of the conjugacy problem in cyclic amalgamations. We revise and prove some theorems of Lipschutz and show their application to cyclic amalgamations of braid groups. We generalize this application to prove a new theorem regarding the conjugacy problem in cyclic amalgamations. We then discuss some application of braid groups, culminating in a section devoted to the discussion of braid group cryptography.

Biographie de l'auteur

Dr. Elie Feder received his Ph.D. from the Graduate Center of City University of New York (CUNY) in 2003. He is currently an assistant professor at Kingsborough Community College of CUNY. His areas of research include: graph theory, combinatorics and combinatorial group theory.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
VDM Verlag Dr. Müller
Date d'édition
2009
Langue
anglais
ISBN 10 
3639138988
ISBN 13 
9783639138986
Reliure
Broché
Nombre de pages
84
Coordonnées du fabricant
non disponible
Personne responsable
non disponible