Topics in Geometric Group Theory Paperback - 2000 - 1st Edition
by Pierre de la Harpe
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From the rear cover
Groups as abstract structures were first recognized by mathematicians in the nineteenth century. Groups are, of course, sets given with appropriate multiplications, and they are often given together with actions on interesting geometric objects. But groups are also interesting geometric objects by themselves. More precisely, a finitely-generated group can be seen as a metric space, the distance between two points being defined up to quasi-isometry by some word length, and this gives rise to a very fruitful approach to group theory. In this book, Pierre de la Harpe provides a concise and engaging introduction to this approach, a new method for studying infinite groups via their intrinsic geometry that has played a major role in mathematics over the past two decades. A recognized expert in the field, de la Harpe uses a hands-on presentation style, illustrating key concepts of geometric group theory with numerous concrete examples. The first five chapters present basic combinatorial and geometric group theory in a unique way, with an emphasis on finitely-generated versus finitely-presented groups. In the final three chapters, de la Harpe discusses new material on the growth of groups, including a detailed treatment of the Grigorchuk group, an infinite finitely-generated torsion group of intermediate growth which is becoming more and more important in group theory. Most sections are followed by exercises and a list of problems and complements, enhancing the book's value for students; problems range from slightly more difficult exercises to open research questions in the field. An extensive list of references directs readers to more advanced results as well as connections with other subjects.
Details
- Title Topics in Geometric Group Theory
- Author Pierre de la Harpe
- Binding Paperback
- Edition number 1st
- Edition 1
- Pages 310
- Volumes 1
- Language ENG
- Publisher University of Chicago Press
- Date 2000-09-15
- ISBN 9780226317212 / 0226317218
- Weight 0.9 lbs (0.41 kg)
- Dimensions 9.01 x 6.05 x 0.69 in (22.89 x 15.37 x 1.75 cm)
- Library of Congress subjects Geometric group theory
- Library of Congress Catalog Number 00020271
- Dewey Decimal Code 512.2
Media reviews
Citations
- Choice, 05/01/2001, Page 1657
- Scitech Book News, 03/01/2001, Page 36
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Topics in Geometric Group Theory
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