Topics in Geometric Group Theory (Chicago Lectures in Mathematics)
| Author | : | |
| Rating | : | 4.36 (615 Votes) |
| Asin | : | 0226317218 |
| Format Type | : | paperback |
| Number of Pages | : | 310 Pages |
| Publish Date | : | 2013-06-24 |
| Language | : | English |
DESCRIPTION:
Worst index ever. Worst index ever. There are no page numbers numbers referencing where to find the subject you are looking for. Only Chapter and then number of the example and/or theorem. Tons of information, no order in which to find it. If there was an order, I missed it which is entirely possible.. "I can't recommend it enough" according to jerbearmy. If I had to give a one sentence review of this book, it would simply be "Read this book to get smarter." I'm a little less than half-way through a casual reading of it, but I can already tell that it's a book that will be worth it no matter how much time I come back and devote to it.Where this book really shines is in the staggering number of examples, both in the exercises and in the text itself. Many math books suffer from a lack of examples, and
In the final three chapters, de la Harpe discusses new material on the growth of groups, including a detailed treatment of the "Grigorchuk group." 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 problems in the field. An extensive list of references directs readers to more advanced results as well as connections with other fields.. A recognized expert in the field, de la Harpe adopts a hands-on approach, illustrating key concepts with numerous concrete examples.The first five chapters present basic combinatorial and geometric group theory in a unique and refreshing way, with an emphasis on finitely generated versus finitely presented groups. In this book, Pierre de la Harpe provides a concise and engaging introduction to geometric group theory, a new method for studying infinite groups via their intrinsic geometry that has played a major role in mathematics over the past two decades
But groups are also interesting geometric objects by themselves. Groups are, of course, sets given with appropriate "multiplications," and they are often given together with actions on interesting geometric objects. 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 decad