Geometric Group Theory (Colloquium Publications) by Cornelia Drutu (PDF)

Description

The key idea in geometric group theory is to study infinite groups by endowing them with a metric and treating them as geometric spaces. This applies to many groups naturally appearing in topology, geometry, and algebra, such as fundamental groups of manifolds, groups of matrices with integer coefficients, etc. The primary focus of this book is to cover the foundations of geometric group theory, including coarse topology, ultralimits and asymptotic cones, hyperbolic groups, isoperimetric inequalities, growth of groups, amenability, Kazhdan’s Property (T) and the Haagerup property, as well as their characterizations in terms of group actions on median spaces and spaces with walls. The book contains proofs of several fundamental results of geometric group theory, such as Gromov’s theorem on groups of polynomial growth, Tits’s alternative, Stallings’s theorem on ends of groups, Dunwoody’s accessibility theorem, the Mostow Rigidity Theorem, and quasiisometric rigidity theorems of Tukia and Schwartz. This is the first book in which geometric group theory is presented in a form accessible to advanced graduate students and young research mathematicians. It fills a big gap in the literature and will be used by researchers in geometric group theory and its applications.

User’s Reviews

Editorial Reviews: Review It will undoubtedly be an essential reference for those working in GGT and related areas in differential geometry and topology. Its wealth of immensely valuable historical commentary is particularly appreciated. –Scott Taylor, MAA Reviews[This book] offers a comprehensive account of major developments in geometric group theory in the 20th century. It is inevitable that some topics are mentioned only briefly, which is compensated by the extensive bibliography of over 600 references, both old and recent. –Igor Belegradek, Mathematical Reviews About the Author Cornelia Drutu, Mathematical Institute, Oxford, United Kingdom.Michael Kapovich, University of California, Davis, CA.

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