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"Geometric group theory is the study of the interplay between groups and the spaces they act on, and has its roots in the works of Henri Poincaré, Felix Klein, J.H.C. Whitehead, and Max Dehn. Office Hours with a Geometric Group Theorist brings together leading experts who provide one-on-one instruction on key topics in this exciting and relatively new field of mathematics. It's like having office hours with your most trusted math professors. An essential primer for undergraduates making the leap to graduate work, the book begins with free groups-actions of free groups on trees, algorithmic questions about free groups, the ping-pong lemma, and automorphisms of free groups. It goes on to cover several large-scale geometric invariants of groups, including quasi-isometry groups, Dehn functions, Gromov hyperbolicity, and asymptotic dimension. It also delves into important examples of groups, such as Coxeter groups, Thompson's groups, right-angled Artin groups, lamplighter groups, mapping class groups, and braid groups. The tone is conversational throughout, and the instruction is driven by examples. Accessible to students who have taken a first course in abstract algebra, Office Hours with a Geometric Group Theorist also features numerous exercises and in-depth projects designed to engage readers and provide jumping-off points for research projects." [Back cover]

Geometric group theory --- Group theory --- Groupes, Théorie géométrique des. --- Geometric group theory.

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Geometric group theory. --- Linear algebraic groups. --- Groupes, Théorie géométrique des --- Groupes linéaires algébriques --- Geometric group theory --- Linear algebraic groups --- Groupes, Théorie géométrique des --- Groupes linéaires algébriques

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Group theory --- Topology --- Geometric group theory. --- Low-dimensional topology. --- Groupes, Théorie géométrique des --- Topologie de basse dimension --- 51 <082.1> --- Mathematics--Series --- Groupes, Théorie géométrique des --- Geometric group theory --- Low-dimensional topology --- Topology, Low-dimensional --- Algebraic topology --- Manifolds (Mathematics)

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Geometry --- Group theory --- 512.54 --- Mathematics --- Euclid's Elements --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- 512.54 Groups. Group theory --- Groups. Group theory --- Geometry. --- Group theory. --- Groupes, Théorie des. --- Geometric group theory --- Groupes, Théorie géométrique des --- Groupes, Théorie des --- Géometrie --- Géometrie --- Groupes, Théorie des. --- Groupes, Théorie des --- Groupes, Théorie géométrique des

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The purpose of this book is to describe the global properties of complete simply­ connected spaces that are non-positively curved in the sense of A. D. Alexandrov and to examine the structure of groups that act properly on such spaces by isometries. Thus the central objects of study are metric spaces in which every pair of points can be joined by an arc isometric to a compact interval of the real line and in which every triangle satisfies the CAT(O) inequality. This inequality encapsulates the concept of non-positive curvature in Riemannian geometry and allows one to reflect the same concept faithfully in a much wider setting - that of geodesic metric spaces. Because the CAT(O) condition captures the essence of non-positive curvature so well, spaces that satisfy this condition display many of the elegant features inherent in the geometry of non-positively curved manifolds. There is therefore a great deal to be said about the global structure of CAT(O) spaces, and also about the structure of groups that act on them by isometries - such is the theme of this book. 1 The origins of our study lie in the fundamental work of A. D. Alexandrov .

Espaces métriques --- Geometry [Differential ] --- Géométrie différentielle --- Meetkunde [Differentiaal] --- Metric spaces --- Ruimten [Metrische ] --- Geometry, Differential --- 514.764.2 --- Spaces, Metric --- Generalized spaces --- Set theory --- Topology --- Differential geometry --- Riemannian and pseudo-Riemannian spaces --- Geometry, Differential. --- Metric spaces. --- 514.764.2 Riemannian and pseudo-Riemannian spaces --- Geometric group theory --- Groupes, Théorie géométrique des --- Topology. --- Manifolds (Mathematics). --- Complex manifolds. --- Group theory. --- Manifolds and Cell Complexes (incl. Diff.Topology). --- Group Theory and Generalizations. --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Analytic spaces --- Manifolds (Mathematics) --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Algebras, Linear --- Groupes, Théorie géométrique des. --- Géometrie différentielle globale --- Géometrie différentielle globale --- Topologie differentielle --- Groupes, Théorie géométrique des.