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Topologie --- Connexions (mathématiques) --- Topology --- Connections (Mathematics) --- Géométrie --- Polytopes --- Geometry --- Embeddings (Mathematics) --- Plongements (mathématiques)

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"This monograph is a contribution to the study of the subgroup structure of exceptional algebraic groups over algebraically closed fields of arbitrary characteristic. Following Serre, a closed subgroup of a semisimple algebraic group G is called irreducible if it lies in no proper parabolic subgroup of G. In this paper we complete the classification of irreducible connected subgroups of exceptional algebraic groups, providing an explicit set of representatives for the conjugacy classes of such subgroups. Many consequences of this classification are also given. These include results concerning the representations of such subgroups on various G-modules: for example, the conjugacy classes of irreducible connected subgroups are determined by their composition factors on the adjoint module of G, with one exception. A result of Liebeck and Testerman shows that each irreducible connected subgroup X of G has only finitely many overgroups and hence the overgroups of X form a lattice. We provide tables that give representatives of each conjugacy class of connected overgroups within this lattice structure. We use this to prove results concerning the subgroup structure of G: for example, when the characteristic is 2, there exists a maximal connected subgroup of G containing a conjugate of every irreducible subgroup A1 of G"--

Linear algebraic groups. --- Representations of groups. --- Embeddings (Mathematics) --- Maximal subgroups. --- Groupes algébriques linéaires --- Représentations de groupes --- Plongements (mathématiques)

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Group theory --- Frattini subgroups. --- Conjugacy classes. --- Embeddings (Mathematics) --- Plongements (mathématiques) --- Conjugacy classes --- Frattini subgroups --- Subgroups, Frattini --- Maximal subgroups --- Imbeddings (Mathematics) --- Geometry, Algebraic --- Immersions (Mathematics) --- Classes of conjugate elements

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Numerical solutions of differential equations --- Boundary value problems --- Initial value problems --- Invariant imbedding. --- Functional equations --- Invariants --- Mathematical physics --- Radiation --- Problems, Initial value --- Differential equations --- Boundary conditions (Differential equations) --- Functions of complex variables --- Data processing. --- Invariant imbedding --- Data processing --- Embeddings (Mathematics) --- Plongements (mathématiques) --- Boundary value problems - Data processing --- Initial value problems - Data processing

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Cuts and metrics are well-known objects that arise - independently, but with many deep and fascinating connections - in diverse fields: in graph theory, combinatorial optimization, geometry of numbers, distance geometry, combinatorial matrix theory, statistical physics, VLSI design etc. A main feature of this book is its interdisciplinarity. The book contains a wealth of results, from different mathematical disciplines, which are presented here in a unified and comprehensive manner. Geometric representations and methods turn out to be the linking theme. This book will provide a unique and invaluable source for researchers and graduate students. From the Reviews: "This book is definitely a milestone in the literature of integer programming and combinatorial optimization. It draws from the interdisciplinarity of these fields as it gathers methods and results from polytope theory, geometry of numbers, probability theory, design and graph theory around two objects, cuts and metrics. [… ] The book is very nicely written [… ] The book is also very well structured. With knowledge about the relevant terms, one can enjoy special subsections without being entirely familiar with the rest of the chapter. This makes it not only an interesting research book but even a dictionary. [… ] In my opinion, the book is a beautiful piece of work. The longer one works with it, the more beautiful it becomes." Robert Weismantel, Optima 56 (1997) "… In short, this is a very interesting book which is nice to have." Alexander I. Barvinok, MR 1460488 (98g:52001) "… This is a large and fascinating book. As befits a book which contains material relevant to so many areas of mathematics (and related disciplines such as statistics, physics, computing science, and economics), it is self-contained and written in a readable style. Moreover, the index, bibliography, and table of contents are all that they should be in such a work; it is easy to find as much or as little introductory material as needed." R.Dawson, Zentralblatt MATH Database 0885.52001.

Discrete mathematics --- Graph theory --- Metric spaces --- Embeddings (Mathematics) --- Théorie des graphes --- Espaces métriques --- Plongements (Mathématiques) --- Graph theory. --- Metric spaces. --- Embeddings (Mathematics). --- Théorie des graphes --- Espaces métriques --- Plongements (Mathématiques) --- Discrete mathematics. --- Geometry. --- Combinatorics. --- Convex geometry . --- Discrete geometry. --- Number theory. --- Discrete Mathematics. --- Graph Theory. --- Convex and Discrete Geometry. --- Number Theory. --- Number study --- Numbers, Theory of --- Algebra --- Geometry --- Combinatorial geometry --- Combinatorics --- Mathematical analysis --- Graphs, Theory of --- Theory of graphs --- Combinatorial analysis --- Topology --- Mathematics --- Euclid's Elements --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis --- Extremal problems