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Four-manifolds (Topology) --- 4-dimensional manifolds (Topology) --- 4-manifolds (Topology) --- Four dimensional manifolds (Topology) --- Manifolds, Four dimensional --- Differential geometry. Global analysis --- Low-dimensional topology --- Topological manifolds

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Differential geometry. Global analysis --- Flows (Differentiable dynamical systems) --- Four-manifolds (Topology) --- Hamiltonian systems --- Hamiltonian dynamical systems --- Systems, Hamiltonian --- Differentiable dynamical systems --- 4-dimensional manifolds (Topology) --- 4-manifolds (Topology) --- Four dimensional manifolds (Topology) --- Manifolds, Four dimensional --- Low-dimensional topology --- Topological manifolds --- Flots (dynamique différentiable) --- Hamiltonian systems. --- Systèmes hamiltoniens --- Systèmes hamiltoniens.

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Differential geometry. Global analysis --- Four-manifolds (Topology) --- Instantons --- 515.16 --- Field theory (Physics) --- Gauge fields (Physics) --- Renormalization (Physics) --- Wave equation --- 4-dimensional manifolds (Topology) --- 4-manifolds (Topology) --- Four dimensional manifolds (Topology) --- Manifolds, Four dimensional --- Low-dimensional topology --- Topological manifolds --- Topology of manifolds --- Instantons. --- Four-manifolds (Topology). --- 515.16 Topology of manifolds

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This book describes work, largely that of the author, on the characterization of closed 4-manifolds in terms of familiar invariants such as Euler characteristic, fundamental group, and Stiefel-Whitney classes. Using techniques from homological group theory, the theory of 3-manifolds and topological surgery, infrasolvmanifolds are characterized up to homeomorphism, and surface bundles are characterized up to simple homotopy equivalence. Non-orientable cases are also considered wherever possible, and in the final chapter the results obtained earlier are applied to 2-knots and complex analytic surfaces. This book is essential reading for anyone interested in low-dimensional topology.

Four-manifolds (Topology) --- Homotopy theory. --- Deformations, Continuous --- Topology --- 4-dimensional manifolds (Topology) --- 4-manifolds (Topology) --- Four dimensional manifolds (Topology) --- Manifolds, Four dimensional --- Low-dimensional topology --- Topological manifolds --- Homotopy theory --- 512.7 --- 512.7 Algebraic geometry. Commutative rings and algebras --- Algebraic geometry. Commutative rings and algebras --- Algebraic topology

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The present book is the first of its kind in dealing with topological quantum field theories and their applications to topological aspects of four manifolds. It is not only unique for this reason but also because it contains sufficient introductory material that it can be read by mathematicians and theoretical physicists. On the one hand, it contains a chapter dealing with topological aspects of four manifolds, on the other hand it provides a full introduction to supersymmetry. The book constitutes an essential tool for researchers interested in the basics of topological quantum field theory, since these theories are introduced in detail from a general point of view. In addition, the book describes Donaldson theory and Seiberg-Witten theory, and provides all the details that have led to the connection between these theories using topological quantum field theory. It provides a full account of Witten’s magic formula relating Donaldson and Seiberg-Witten invariants. Furthermore, the book presents some of the recent developments that have led to important applications in the context of the topology of four manifolds.

Quantum field theory. --- Four-manifolds (Topology) --- 4-dimensional manifolds (Topology) --- 4-manifolds (Topology) --- Four dimensional manifolds (Topology) --- Manifolds, Four dimensional --- Low-dimensional topology --- Topological manifolds --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Topology. --- Global differential geometry. --- Theoretical, Mathematical and Computational Physics. --- Differential Geometry. --- Geometry, Differential --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Mathematical physics. --- Differential geometry. --- Differential geometry --- Physical mathematics --- Physics --- Mathematics