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.
(3) If f, (3) = b and d is a direction based at a then • For some m > 0, j"(a) e Fix(g). • f,(g"(a)) and Df,(Dg" (d)) are independent of k > 0. (4) The assignment (p → b = Fix(pl.) of (1) defines a bijection between PA(Q) and the set ...
Timothy C. Burness,, Soumaïa Ghandour, Donna M. Testerman. Rough description C1 Stabilizers ... The Ci collections that the Jordan normal form of x on W comprises an even number of unipotent Jordan blocks of size 2 (see [2, Section 8]).
Am. Math. Soc. 112 (1991), no. 2, 549–562. Laurent Bartholdi, The growth of Grigorchuk's torsion group, Internat. Math. ... and Palle E. T. Jorgensen, Iterated function systems and permutation representations of the Cuntz algebra, vol.
An extended tour through a selection of the most important trends in modern geometric group theory.
... 2011 Palle E. T. Jorgensen, Keri A. Kornelson, and Karen L. Shuman, Iterated function systems, moments, and transformations of infinite matrices, 2011 Man Chun Leung, Supported blow-up and prescribed scalar curvature on Sn, ...