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Algebraic topology --- Knot theory --- Nœuds, Théorie des --- Statistical methods --- Méthodes statistiques --- Knot theory - Statistical methods --- Nœuds, Théorie des - Méthodes statistiques

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Algebraic topology --- Category theory. Homological algebra --- K-theory. --- Knot theory. --- Cobordism theory. --- K-théorie --- Noeuds, Théorie des --- Cobordismes, Théorie des --- Cobordism theory --- Knot theory --- K-theory --- Homology theory --- Knots (Topology) --- Low-dimensional topology --- Differential topology --- K-théorie. --- Noeuds, Théorie des. --- Cobordismes, Théorie des.

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Ordered algebraic structures --- Fiber spaces (Mathematics) --- Homotopy theory --- Knot theory --- Manifolds (Mathematics) --- Geometry, Differential --- Topology --- Knots (Topology) --- Low-dimensional topology --- Deformations, Continuous --- Fibre spaces (Mathematics) --- Algebraic topology --- Homotopy theory. --- Knot theory. --- Noeuds, Théorie des. --- Homotopie. --- Espaces fibrés (mathématiques)

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The closed orbits of three-dimensional flows form knots and links. This book develops the tools - template theory and symbolic dynamics - needed for studying knotted orbits. This theory is applied to the problems of understanding local and global bifurcations, as well as the embedding data of orbits in Morse-smale, Smale, and integrable Hamiltonian flows. The necesssary background theory is sketched; however, some familiarity with low-dimensional topology and differential equations is assumed.

Differential geometry. Global analysis --- Flows (Differentiable dynamical systems) --- Knot theory --- Link theory --- Geometry --- Mathematical Theory --- Mathematics --- Physical Sciences & Mathematics --- Flows (Differentieerbare systemen) --- Flows (Systèmes dynamiques différentiables) --- Knopentheorie --- Noeuds [Theorie des ] --- Manifolds (Mathematics). --- Complex manifolds. --- Manifolds and Cell Complexes (incl. Diff.Topology). --- Analytic spaces --- Manifolds (Mathematics) --- Geometry, Differential --- Topology --- Link theory. --- Knot theory. --- Knots (Topology) --- Low-dimensional topology --- Piecewise linear topology

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This book is an introduction to the theory of knots via the theory of braids, which attempts to be complete in a number of ways. Some knowledge of Topology is assumed. Necessary Group Theory and further necessary Topology are given in the book. The exposition is intended to enable an interested reader to learn the basics of the subject. Emphasis is placed on covering the theory in an algebraic way. The work includes quite a number of worked examples. The latter part of the book is devoted to previously unpublished material.

Noeuds, théorie des. --- Tresses, théorie des. --- Manifolds. --- Knot theory. --- Braid theory. --- Théorie des noeuds --- Tresses, Théorie des --- Knot theory --- Braid theory --- 515.16 --- Knots (Topology) --- Low-dimensional topology --- Braids, Theory of --- Theory of braids --- Topology of manifolds --- 515.16 Topology of manifolds