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The book, suitable as both an introductory reference and as a text book in the rapidly growing field of topological graph theory, models both maps (as in map-coloring problems) and groups by means of graph imbeddings on sufaces. Automorphism groups of both graphs and maps are studied. In addition connections are made to other areas of mathematics, such as hypergraphs, block designs, finite geometries, and finite fields. There are chapters on the emerging subfields of enumerative topological graph theory and random topological graph theory, as well as a chapter on the composition of English

Topological graph theory. --- Graph theory --- Topology

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Lie groups --- Mathematical Theory --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Lie groups. --- Lie [Groepen van ] --- Lie [Groupes de ] --- 512.54 --- 512.54 Groups. Group theory --- Groups. Group theory --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Topological groups. --- Mathematical analysis. --- Analysis (Mathematics). --- Algebraic geometry. --- Topological Groups, Lie Groups. --- Analysis. --- Algebraic Geometry. --- Algebraic geometry --- Geometry --- 517.1 Mathematical analysis --- Mathematical analysis --- Groups, Topological --- Continuous groups

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Recent research has repeatedly led to connections between important rigidity questions and bounded cohomology. However, the latter has remained by and large intractable. This monograph introduces the functorial study of the continuous bounded cohomology for topological groups, with coefficients in Banach modules. The powerful techniques of this more general theory have successfully solved a number of the original problems in bounded cohomology. As applications, one obtains, in particular, rigidity results for actions on the circle, for representations on complex hyperbolic spaces and on Teichmüller spaces. A special effort has been made to provide detailed proofs or references in quite some generality.

Locally compact groups --- Homology theory --- Calculus --- Mathematical Theory --- Mathematics --- Physical Sciences & Mathematics --- Locally compact groups. --- Homology theory. --- Groupes localement compacts --- Homologie --- Lokaal compacte groepen --- Cohomology theory --- Contrahomology theory --- Algebraic topology --- Compact groups --- Topological groups --- Algebraic topology. --- Topological groups. --- Lie groups. --- Group theory. --- Algebraic Topology. --- Topological Groups, Lie Groups. --- Group Theory and Generalizations. --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Groups, Topological --- Continuous groups --- Topology

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'Optimal Solution of Nonlinear Equations' is a text/monograph designed to provide an overview of optimal computational methods for the solution of nonlinear equations, fixed points of contractive and noncontractive mapping and for the computation of the topological degree. It is of interest to any reader working in the area of information-based complexity.

Differential equations, Nonlinear --- Mathematical optimization. --- Fixed point theory. --- Topological degree. --- Degree, Topological --- Degree (Topology) --- Degree theory --- Algebraic topology --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Fixed point theorems (Topology) --- Nonlinear operators --- Coincidence theory (Mathematics) --- Numerical analysis --- Numerical solutions. --- Fixed point theory --- Mathematical optimization --- Topological degree --- Differential equations, Nonlinear - Numerical solutions --- Analyse numérique. --- Équations. --- Théories non linéaires. --- Equations --- Nonlinear theories --- Topologie algébrique. --- Degré topologique.

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Topological groups. Lie groups --- Hyperbolic groups. --- Groupes hyperboliques --- Tiling (Mathematics) --- Pavage (mathématiques) --- Cancellation theory (Group theory) --- Hyperbolic groups --- Combinatorial designs and configurations --- Mathematics --- Group theory --- Groupes hyperboliques.