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Algebraic topology --- Group theory --- Topological manifolds
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Probabilities --- Linear topological spaces --- Gaussian processes
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The concept of topology has become commonplace in various scientific fields. This volume contains articles on experiments and theories in connection with topology, including fields such as materials science, superconductivity, charge density waves, superfluidity, optics, and field theory.
Topological defects (Physics) --- Topology --- Defects, Topological (Physics) --- Phase rule and equilibrium
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Probabilities --- Linear topological spaces --- Gaussian processes --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Topological linear spaces --- Topological vector spaces --- Vector topology --- Topology --- Vector spaces --- Distribution (Probability theory) --- Stochastic processes
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The aim of this book is to give an overview of selected topics on the topology of real and complex isolated singularities, with emphasis on its relations to other branches of geometry and topology. The first chapters are mostly devoted to complex singularities and a myriad of results spread in a vast literature, which are presented here in a unified way, accessible to non-specialists. Among the topics are the fibration theorems of Milnor; the relation with 3-dimensional Lie groups; exotic spheres; spin structures and 3-manifold invariants; the geometry of quadrics and Arnold's theorem which states that the complex projective plane modulo conjugation is the 4-sphere. The second part of the book studies pioneer work about real analytic singularities which arise from the topological and geometric study of holomorphic vector fields and foliations. In the low dimensional case these turn out to be related to fibred links in the 3-sphere defined by meromorphic functions. This provides new methods for constructing manifolds equipped with a rich geometry. The book is largely self-contained and serves a wide audience of graduate students, mathematicians and researchers interested in geometry and topology.
Topological groups. Lie groups --- Functional analysis --- topologie (wiskunde) --- functies (wiskunde)
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Groupes et algèbres de Lie, Chapitres 2 et 3 Les Éléments de mathématique de Nicolas BOURBAKI ont pour objet une présentation rigoureuse, systématique et sans prérequis des mathématiques depuis leurs fondements. Ce deuxième volume du Livre sur les Groupes et algèbres de Lie, neuvième Livre du traité, comprend les chapitres : 2. Algèbres de Lie libres ; 3. Groupes de Lie. Le chapitre 2 poursuit la présentation des notions fondamentales des algèbres de Lie avec l'introduction des algèbres de Lie libres et de la série de Hausdorff. Le chapitre 3 est consacré aux concepts de base pour les groupes de Lies sur un corps archimédien ou ultramétrique. Ce volume contient également de notes historiques pour les chapitres 1 à 3. Ce volume est une réimpression de l'édition de 1972.
Ordered algebraic structures --- Topological groups. Lie groups --- algebra --- topologie (wiskunde)
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Ordered algebraic structures --- Topological groups. Lie groups --- algebra --- topologie (wiskunde)
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