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One of the great achievements of contemporary mathematics is the new understanding of four dimensions. Michael Freedman and Frank Quinn have been the principals in the geometric and topological development of this subject, proving the Poincar and Annulus conjectures respectively. Recognition for this work includes the award of the Fields Medal of the International Congress of Mathematicians to Freedman in 1986. In Topology of 4-Manifolds these authors have collaborated to give a complete and accessible account of the current state of knowledge in this field. The basic material has been considerably simplified from the original publications, and should be accessible to most graduate students. The advanced material goes well beyond the literature; nearly one-third of the book is new. This work is indispensable for any topologist whose work includes four dimensions. It is a valuable reference for geometers and physicists who need an awareness of the topological side of the field.Originally published in 1990.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Differential topology --- Four-manifolds (Topology) --- Trois-variétés (Topologie) --- Vier-menigvuldigheden (Topologie) --- 4-dimensional manifolds (Topology) --- 4-manifolds (Topology) --- Four dimensional manifolds (Topology) --- Manifolds, Four dimensional --- Low-dimensional topology --- Topological manifolds --- 4-manifold. --- Ambient isotopy. --- Annulus theorem. --- Automorphism. --- Baire category theorem. --- Bilinear form. --- Boundary (topology). --- CW complex. --- Category of manifolds. --- Central series. --- Characterization (mathematics). --- Cohomology. --- Commutative diagram. --- Commutative property. --- Commutator subgroup. --- Compactification (mathematics). --- Conformal geometry. --- Connected sum. --- Connectivity (graph theory). --- Cyclic group. --- Diagram (category theory). --- Diameter. --- Diffeomorphism. --- Differentiable manifold. --- Differential geometry. --- Dimension. --- Disk (mathematics). --- Duality (mathematics). --- Eigenvalues and eigenvectors. --- Embedding problem. --- Embedding. --- Equivariant map. --- Fiber bundle. --- Four-dimensional space. --- Fundamental group. --- General position. --- Geometry. --- H-cobordism. --- Handlebody. --- Hauptvermutung. --- Homeomorphism. --- Homology (mathematics). --- Homology sphere. --- Homomorphism. --- Homotopy group. --- Homotopy sphere. --- Homotopy. --- Hurewicz theorem. --- Hyperbolic geometry. --- Hyperbolic group. --- Hyperbolic manifold. --- Identity matrix. --- Intermediate value theorem. --- Intersection (set theory). --- Intersection curve. --- Intersection form (4-manifold). --- Intersection number (graph theory). --- Intersection number. --- J-homomorphism. --- Knot theory. --- Lefschetz duality. --- Line–line intersection. --- Manifold. --- Mapping cylinder. --- Mathematical induction. --- Metric space. --- Metrization theorem. --- Module (mathematics). --- Normal bundle. --- Parametrization. --- Parity (mathematics). --- Product topology. --- Pullback (differential geometry). --- Regular homotopy. --- Ring homomorphism. --- Rotation number. --- Seifert–van Kampen theorem. --- Sesquilinear form. --- Set (mathematics). --- Simply connected space. --- Smooth structure. --- Special case. --- Spin structure. --- Submanifold. --- Subset. --- Support (mathematics). --- Tangent bundle. --- Tangent space. --- Tensor product. --- Theorem. --- Topological category. --- Topological manifold. --- Transversal (geometry). --- Transversality (mathematics). --- Transversality theorem. --- Uniqueness theorem. --- Unit disk. --- Vector bundle. --- Whitehead torsion. --- Whitney disk.

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This book offers a self-contained account of the 3-manifold invariants arising from the original Jones polynomial. These are the Witten-Reshetikhin-Turaev and the Turaev-Viro invariants. Starting from the Kauffman bracket model for the Jones polynomial and the diagrammatic Temperley-Lieb algebra, higher-order polynomial invariants of links are constructed and combined to form the 3-manifold invariants. The methods in this book are based on a recoupling theory for the Temperley-Lieb algebra. This recoupling theory is a q-deformation of the SU(2) spin networks of Roger Penrose. The recoupling theory is developed in a purely combinatorial and elementary manner. Calculations are based on a reformulation of the Kirillov-Reshetikhin shadow world, leading to expressions for all the invariants in terms of state summations on 2-cell complexes. Extensive tables of the invariants are included. Manifolds in these tables are recognized by surgery presentations and by means of 3-gems (graph encoded 3-manifolds) in an approach pioneered by Sostenes Lins. The appendices include information about gems, examples of distinct manifolds with the same invariants, and applications to the Turaev-Viro invariant and to the Crane-Yetter invariant of 4-manifolds.

Drie-menigvuldigheden (Topologie) --- Knopentheorie --- Knot theory --- Noeuds [Theorie des ] --- Three-manifolds (Topology) --- Trois-variétés (Topologie) --- Knot theory. --- Algebraic topology --- Invariants --- Mathematics --- Invariants (Mathematics) --- Invariants. --- 3-manifolds (Topology) --- Manifolds, Three dimensional (Topology) --- Three-dimensional manifolds (Topology) --- Low-dimensional topology --- Topological manifolds --- Knots (Topology) --- 3-manifold. --- Addition. --- Algorithm. --- Ambient isotopy. --- Axiom. --- Backslash. --- Barycentric subdivision. --- Bijection. --- Bipartite graph. --- Borromean rings. --- Boundary parallel. --- Bracket polynomial. --- Calculation. --- Canonical form. --- Cartesian product. --- Cobordism. --- Coefficient. --- Combination. --- Commutator. --- Complex conjugate. --- Computation. --- Connected component (graph theory). --- Connected sum. --- Cubic graph. --- Diagram (category theory). --- Dimension. --- Disjoint sets. --- Disjoint union. --- Elaboration. --- Embedding. --- Equation. --- Equivalence class. --- Explicit formula. --- Explicit formulae (L-function). --- Factorial. --- Fundamental group. --- Graph (discrete mathematics). --- Graph embedding. --- Handlebody. --- Homeomorphism. --- Homology (mathematics). --- Identity element. --- Intersection form (4-manifold). --- Inverse function. --- Jones polynomial. --- Kirby calculus. --- Line segment. --- Linear independence. --- Matching (graph theory). --- Mathematical physics. --- Mathematical proof. --- Mathematics. --- Maxima and minima. --- Monograph. --- Natural number. --- Network theory. --- Notation. --- Numerical analysis. --- Orientability. --- Orthogonality. --- Pairing. --- Pairwise. --- Parametrization. --- Parity (mathematics). --- Partition function (mathematics). --- Permutation. --- Poincaré conjecture. --- Polyhedron. --- Quantum group. --- Quantum invariant. --- Recoupling. --- Recursion. --- Reidemeister move. --- Result. --- Roger Penrose. --- Root of unity. --- Scientific notation. --- Sequence. --- Significant figures. --- Simultaneous equations. --- Smoothing. --- Special case. --- Sphere. --- Spin network. --- Summation. --- Symmetric group. --- Tetrahedron. --- The Geometry Center. --- Theorem. --- Theory. --- Three-dimensional space (mathematics). --- Time complexity. --- Tubular neighborhood. --- Two-dimensional space. --- Vector field. --- Vector space. --- Vertex (graph theory). --- Winding number. --- Writhe.

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Surgery theory, the basis for the classification theory of manifolds, is now about forty years old. There have been some extraordinary accomplishments in that time, which have led to enormously varied interactions with algebra, analysis, and geometry. Workers in many of these areas have often lamented the lack of a single source that surveys surgery theory and its applications. Indeed, no one person could write such a survey. The sixtieth birthday of C. T. C. Wall, one of the leaders of the founding generation of surgery theory, provided an opportunity to rectify the situation and produce a comprehensive book on the subject. Experts have written state-of-the-art reports that will be of broad interest to all those interested in topology, not only graduate students and mathematicians, but mathematical physicists as well. Contributors include J. Milnor, S. Novikov, W. Browder, T. Lance, E. Brown, M. Kreck, J. Klein, M. Davis, J. Davis, I. Hambleton, L. Taylor, C. Stark, E. Pedersen, W. Mio, J. Levine, K. Orr, J. Roe, J. Milgram, and C. Thomas.

Chirurgie (Topologie) --- Heelkunde (Topologie) --- Surgery (Topology) --- Differential topology --- Homotopy equivalences --- Manifolds (Mathematics) --- Topology --- Algebraic topology (object). --- Algebraic topology. --- Ambient isotopy. --- Assembly map. --- Atiyah–Hirzebruch spectral sequence. --- Atiyah–Singer index theorem. --- Automorphism. --- Banach algebra. --- Borsuk–Ulam theorem. --- C*-algebra. --- CW complex. --- Calculation. --- Category of manifolds. --- Characterization (mathematics). --- Chern class. --- Cobordism. --- Codimension. --- Cohomology. --- Compactification (mathematics). --- Conjecture. --- Contact geometry. --- Degeneracy (mathematics). --- Diagram (category theory). --- Diffeomorphism. --- Differentiable manifold. --- Differential geometry. --- Dirac operator. --- Disk (mathematics). --- Donaldson theory. --- Duality (mathematics). --- Embedding. --- Epimorphism. --- Excision theorem. --- Exponential map (Riemannian geometry). --- Fiber bundle. --- Fibration. --- Fundamental group. --- Group action. --- Group homomorphism. --- H-cobordism. --- Handle decomposition. --- Handlebody. --- Homeomorphism group. --- Homeomorphism. --- Homology (mathematics). --- Homomorphism. --- Homotopy extension property. --- Homotopy fiber. --- Homotopy group. --- Homotopy. --- Hypersurface. --- Intersection form (4-manifold). --- Intersection homology. --- Isomorphism class. --- K3 surface. --- L-theory. --- Limit (category theory). --- Manifold. --- Mapping cone (homological algebra). --- Mapping cylinder. --- Mostow rigidity theorem. --- Orthonormal basis. --- Parallelizable manifold. --- Poincaré conjecture. --- Product metric. --- Projection (linear algebra). --- Pushout (category theory). --- Quaternionic projective space. --- Quotient space (topology). --- Resolution of singularities. --- Ricci curvature. --- Riemann surface. --- Riemannian geometry. --- Riemannian manifold. --- Ring homomorphism. --- Scalar curvature. --- Semisimple algebra. --- Sheaf (mathematics). --- Sign (mathematics). --- Special case. --- Sub"ient. --- Subgroup. --- Submanifold. --- Support (mathematics). --- Surgery exact sequence. --- Surgery obstruction. --- Surgery theory. --- Symplectic geometry. --- Symplectic vector space. --- Theorem. --- Topological conjugacy. --- Topological manifold. --- Topology. --- Transversality (mathematics). --- Transversality theorem. --- Vector bundle. --- Waldhausen category. --- Whitehead torsion. --- Whitney embedding theorem. --- Yamabe invariant.