Algorithmic Problems in the Braid Group | Theory and Applications
Elie Feder
ISBN 10: 3639138988 ISBN 13: 9783639138986
Published by VDM Verlag Dr. Müller, 2009
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Algorithmic Problems in the Braid Group | Theory and Applications | Elie Feder | Taschenbuch | Englisch | VDM Verlag Dr. Müller | EAN 9783639138986 | Verantwortliche Person für die EU: VDM Verlag Dr. Müller, Brivibas Gatve 197, 1039 RIGA, LETTLAND, customerservice[at]vdm-vsg[dot]de | Anbieter: preigu. Seller Inventory # 101571706
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.
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Bibliographic Details
Title: Algorithmic Problems in the Braid Group | ...
Publisher: VDM Verlag Dr. Müller
Publication Date: 2009
Binding: Taschenbuch
Condition: Neu