The Geometry of the Word Problem for Finitely Generated Groups (Advanced Courses in Mathematics - CRM Barcelona) - Softcover

Book 3 of 35: Advanced Courses in Mathematics - CRM Barcelona

Brady, Noel; Riley, Tim; Short, Hamish

 
9783764379490: The Geometry of the Word Problem for Finitely Generated Groups (Advanced Courses in Mathematics - CRM Barcelona)
Softcover
ISBN 10: 3764379499 ISBN 13: 9783764379490
Publisher: Birkhäuser, 2006

Synopsis

The origins of the word problem are in group theory, decidability and complexity. But through the vision of M. Gromov and the language of filling functions, the topic now impacts the world of large-scale geometry. This book contains accounts of many recent developments in Geometric Group Theory and shows the interaction between the word problem and geometry continues to be a central theme. It contains many figures, numerous exercises and open questions.

"synopsis" may belong to another edition of this title.

Synopsis

The origins of the word problem are in group theory, decidability and complexity, but, through the vision of M. Gromov and the language of filling functions, the topic now impacts the world of large-scale geometry, including topics such as soap films, isoperimetry, coarse invariants and curvature. The first part introduces van Kampen diagrams in Cayley graphs of finitely generated, infinite groups; it discusses the van Kampen lemma, the isoperimetric functions or Dehn functions, the theory of small cancellation groups and an introduction to hyperbolic groups. One of the main tools in geometric group theory is the study of spaces, in particular geodesic spaces and manifolds, such that the groups act upon. The second part is thus dedicated to Dehn functions, negatively curved groups, in particular, CAT(0) groups, cubings and cubical complexes. In the last part, filling functions are presented from geometric, algebraic and algorithmic points of view, how filling functions interact is discussed, and applications to nilpotent groups, hyperbolic groups and asymptotic cones are given. Many examples and open problems are included.

"About this title" may belong to another edition of this title.

Publisher
Birkhäuser
Publication date
2006
Language
English
ISBN 10 
3764379499
ISBN 13 
9783764379490
Binding
Paperback
Number of pages
215

Other Popular Editions of the Same Title

9783764391676: The Geometry of the Word Problem for Finitely Generated Groups

Featured Edition

ISBN 10:  3764391677 ISBN 13:  9783764391676
Publisher: Springer, 2008
Softcover