Algorithmic Problems in the Braid Group : Theory and Applications

Elie Feder

ISBN 10: 3639138988 / ISBN 13: 9783639138986

Published by VDM Verlag Dr. Müller, 2009

About this Item

nach der Bestellung gedruckt Neuware - Printed after ordering - 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.

Seller Inventory # 9783639138986

Bibliographic Details

• Title: Algorithmic Problems in the Braid Group : Theory and Applications
• Publisher: VDM Verlag Dr. Müller
• Publication Date: 2009
• Language: English
• ISBN 10: 3639138988
• ISBN 13: 9783639138986
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 220W x 150H x 4D millimeters 220 millimeters width by 150 millimeters height by 4 millimeters depth
• Weight: 128 grams

About this title

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.

About the Author

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.