{"product_id":"topics-in-geometric-group-theory-paperback","title":"Topics in Geometric Group Theory - Paperback","description":"\u003cp\u003eby \u003cb\u003ePierre de la Harpe\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003eIn 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. A recognized expert in the field, de la Harpe adopts a hands-on approach, illustrating key concepts with numerous concrete examples. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e 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 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.\u003ch3\u003eFront Jacket\u003c\/h3\u003e\u003cp\u003eGroups 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. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003eIn 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. \u003cp\u003e\u003c\/p\u003eThe 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.\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003e\u003cb\u003ePierre de la Harpe\u003c\/b\u003e is a professor of mathematics at the Université de Genève, Switzerland. He is the author, coauthor, or coeditor of several books, including \u003ci\u003eLa propriété (T) de Kazhdan pour les groupes localement compacts\u003c\/i\u003e and \u003ci\u003eSur les groupes hyperboliques d'après Mikhael Gromov\u003c\/i\u003e.\u003c\/p\u003e\u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 310\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.69 x 9.01 x 6.05 IN\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e September 15, 2000\u003c\/div\u003e","brand":"Books by splitShops","offers":[{"title":"Default Title","offer_id":47454595252402,"sku":"9780226317212","price":75.24,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0770\/3891\/1666\/files\/459cb2d759b02b15306b402d45e93c02_d2c7e95b-ea5c-4573-b785-95117b2db1b3.webp?v=1778855342","url":"https:\/\/box.dadyminds.org\/products\/topics-in-geometric-group-theory-paperback","provider":"DADYMINDS BOX","version":"1.0","type":"link"}