Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

"The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students.The book begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichm©oller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification"--Provided by publisher.

Mappings (Mathematics) --- Class groups (Mathematics) --- Groups, Class (Mathematics) --- Algebraic number theory --- Commutative rings --- Ideals (Algebra) --- Maps (Mathematics) --- Functions --- Functions, Continuous --- Topology --- Transformations (Mathematics) --- 3-manifold theory. --- Alexander method. --- Birman exact sequence. --- BirmanЈilden theorem. --- Dehn twists. --- DehnЌickorish theorem. --- DehnЎielsenЂaer theorem. --- Dennis Johnson. --- Euler class. --- FenchelЎielsen coordinates. --- Gervais presentation. --- Grtzsch's problem. --- Johnson homomorphism. --- Markov partitions. --- Meyer signature cocycle. --- Mod(S). --- Nielsen realization theorem. --- NielsenДhurston classification theorem. --- NielsenДhurston classification. --- Riemann surface. --- Teichmller mapping. --- Teichmller metric. --- Teichmller space. --- Thurston compactification. --- Torelli group. --- Wajnryb presentation. --- algebraic integers. --- algebraic intersection number. --- algebraic relations. --- algebraic structure. --- annulus. --- aspherical manifold. --- bigon criterion. --- braid group. --- branched cover. --- capping homomorphism. --- classifying space. --- closed surface. --- collar lemma. --- compactness criterion. --- complex of curves. --- configuration space. --- conjugacy class. --- coordinates principle. --- cutting homomorphism. --- cyclic subgroup. --- diffeomorphism. --- disk. --- existence theorem. --- extended mapping class group. --- finite index. --- finite subgroup. --- finite-order homeomorphism. --- finite-order mapping class. --- first homology group. --- geodesic laminations. --- geometric classification. --- geometric group theory. --- geometric intersection number. --- geometric operation. --- geometry. --- harmonic maps. --- holomorphic quadratic differential. --- homeomorphism. --- homological criterion. --- homotopy. --- hyperbolic geometry. --- hyperbolic plane. --- hyperbolic structure. --- hyperbolic surface. --- inclusion homomorphism. --- infinity. --- intersection number. --- isotopy. --- lantern relation. --- low-dimensional homology. --- mapping class group. --- mapping torus. --- measured foliation space. --- measured foliations. --- metric geometry. --- moduli space. --- orbifold. --- orbit. --- outer automorphism group. --- pseudo-Anosov homeomorphism. --- punctured disk. --- quasi-isometry. --- quasiconformal map. --- second homology group. --- simple closed curve. --- simplicial complex. --- stretch factors. --- surface bundles. --- surface homeomorphism. --- surface. --- symplectic representation. --- topology. --- torsion. --- torus. --- train track.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Since Poincaré's time, topologists have been most concerned with three species of manifold. The most primitive of these--the TOP manifolds--remained rather mysterious until 1968, when Kirby discovered his now famous torus unfurling device. A period of rapid progress with TOP manifolds ensued, including, in 1969, Siebenmann's refutation of the Hauptvermutung and the Triangulation Conjecture. Here is the first connected account of Kirby's and Siebenmann's basic research in this area.The five sections of this book are introduced by three articles by the authors that initially appeared between 1968 and 1970. Appendices provide a full discussion of the classification of homotopy tori, including Casson's unpublished work and a consideration of periodicity in topological surgery.

Differential geometry. Global analysis --- Manifolds (Mathematics) --- Piecewise linear topology --- Triangulating manifolds --- Variétés (Mathématiques) --- Topologie linéaire par morceaux --- 515.16 --- Manifolds, Triangulating --- PL topology --- Topology --- Geometry, Differential --- Topology of manifolds --- Piecewise linear topology. --- Triangulating manifolds. --- Manifolds (Mathematics). --- 515.16 Topology of manifolds --- Variétés (Mathématiques) --- Topologie linéaire par morceaux --- Triangulation. --- Triangulation --- Affine space. --- Algebraic topology (object). --- Approximation. --- Associative property. --- Automorphism. --- Big O notation. --- CW complex. --- Calculation. --- Cap product. --- Cartesian product. --- Category of sets. --- Chain complex. --- Classification theorem. --- Classifying space. --- Cobordism. --- Codimension. --- Cofibration. --- Cohomology. --- Connected space. --- Continuous function (set theory). --- Continuous function. --- Counterexample. --- Diffeomorphism. --- Differentiable manifold. --- Differential structure. --- Differential topology. --- Dimension (vector space). --- Direct proof. --- Disjoint union. --- Elementary proof. --- Embedding. --- Euclidean space. --- Existence theorem. --- Existential quantification. --- Fiber bundle. --- Fibration. --- General position. --- Geometry. --- Group homomorphism. --- H-cobordism. --- H-space. --- Handle decomposition. --- Handlebody. --- Hauptvermutung. --- Hausdorff space. --- Hilbert cube. --- Homeomorphism group. --- Homeomorphism. --- Homomorphism. --- Homotopy group. --- Homotopy. --- Inclusion map. --- Injective function. --- Invertible matrix. --- K-cell (mathematics). --- Kan extension. --- Linear subspace. --- Linear topology. --- Manifold. --- Mapping cylinder. --- Mathematical induction. --- Mathematician. --- Metric space. --- Morse theory. --- Neighbourhood (mathematics). --- Open set. --- Partition of unity. --- Piecewise linear manifold. --- Piecewise linear. --- Poincaré conjecture. --- Polyhedron. --- Principal bundle. --- Product metric. --- Pushout (category theory). --- Regular homotopy. --- Retract. --- Sheaf (mathematics). --- Simplicial complex. --- Smoothing. --- Spin structure. --- Stability theory. --- Stable manifold. --- Standard map. --- Submanifold. --- Submersion (mathematics). --- Subset. --- Surgery exact sequence. --- Surjective function. --- Theorem. --- Topological group. --- Topological manifold. --- Topological space. --- Topology. --- Transversal (geometry). --- Transversality (mathematics). --- Transversality theorem. --- Union (set theory). --- Uniqueness theorem. --- Vector bundle. --- Zorn's lemma. --- Variétés topologiques

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book presents a new result in 3-dimensional topology. It is well known that any closed oriented 3-manifold can be obtained by surgery on a framed link in S 3. In Global Surgery Formula for the Casson-Walker Invariant, a function F of framed links in S 3 is described, and it is proven that F consistently defines an invariant, lamda (l), of closed oriented 3-manifolds. l is then expressed in terms of previously known invariants of 3-manifolds. For integral homology spheres, l is the invariant introduced by Casson in 1985, which allowed him to solve old and famous questions in 3-dimensional topology. l becomes simpler as the first Betti number increases. As an explicit function of Alexander polynomials and surgery coefficients of framed links, the function F extends in a natural way to framed links in rational homology spheres. It is proven that F describes the variation of l under any surgery starting from a rational homology sphere. Thus F yields a global surgery formula for the Casson invariant.

Chirurgie (Topologie) --- Drie-menigvuldigheden (Topologie) --- Heelkunde (Topologie) --- Surgery (Topology) --- Three-manifolds (Topology) --- Trois-variétés (Topologie) --- 3-manifolds (Topology) --- Manifolds, Three dimensional (Topology) --- Three-dimensional manifolds (Topology) --- Low-dimensional topology --- Topological manifolds --- Differential topology --- Homotopy equivalences --- Manifolds (Mathematics) --- Topology --- 515.16 --- 515.16 Topology of manifolds --- Topology of manifolds --- 3-manifold. --- Addition. --- Alexander polynomial. --- Ambient isotopy. --- Betti number. --- Casson invariant. --- Change of basis. --- Change of variables. --- Cobordism. --- Coefficient. --- Combination. --- Combinatorics. --- Computation. --- Conjugacy class. --- Connected component (graph theory). --- Connected space. --- Connected sum. --- Cup product. --- Determinant. --- Diagram (category theory). --- Disk (mathematics). --- Empty set. --- Exterior (topology). --- Fiber bundle. --- Fibration. --- Function (mathematics). --- Fundamental group. --- Homeomorphism. --- Homology (mathematics). --- Homology sphere. --- Homotopy sphere. --- Indeterminate (variable). --- Integer. --- Klein bottle. --- Knot theory. --- Manifold. --- Morphism. --- Notation. --- Orientability. --- Permutation. --- Polynomial. --- Prime number. --- Projective plane. --- Scientific notation. --- Seifert surface. --- Sequence. --- Summation. --- Symmetrization. --- Taylor series. --- Theorem. --- Topology. --- Tubular neighborhood. --- Unlink.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The description for this book, Knot Groups. Annals of Mathematics Studies. (AM-56), Volume 56, will be forthcoming.

Topology --- 512 --- Algebra --- 512 Algebra --- Knot theory. --- Knots (Topology) --- Low-dimensional topology --- Abelian group. --- Alexander duality. --- Alexander polynomial. --- Algebraic theory. --- Algorithm. --- Analytic continuation. --- Associative property. --- Automorphism. --- Axiom. --- Bijection. --- Binary relation. --- Calculation. --- Central series. --- Characterization (mathematics). --- Cobordism. --- Coefficient. --- Cohomology. --- Combinatorics. --- Commutator subgroup. --- Complete theory. --- Computation. --- Conjugacy class. --- Conjugate element (field theory). --- Connected space. --- Connectedness. --- Coprime integers. --- Coset. --- Covering space. --- Curve. --- Cyclic group. --- Dehn's lemma. --- Determinant. --- Diagonalization. --- Diagram (category theory). --- Dimension. --- Direct product. --- Equivalence class. --- Equivalence relation. --- Euclidean space. --- Euler characteristic. --- Existential quantification. --- Fiber bundle. --- Finite group. --- Finitely generated module. --- Frattini subgroup. --- Free abelian group. --- Fundamental group. --- Geometry. --- Group ring. --- Group theory. --- Group with operators. --- Hausdorff space. --- Homeomorphism. --- Homology (mathematics). --- Homomorphism. --- Homotopy group. --- Homotopy. --- Identity matrix. --- Inner automorphism. --- Interior (topology). --- Intersection number (graph theory). --- Knot group. --- Linear combination. --- Manifold. --- Mathematical induction. --- Monomorphism. --- Morphism. --- Morse theory. --- Natural transformation. --- Non-abelian group. --- Normal subgroup. --- Orientability. --- Permutation. --- Polynomial. --- Presentation of a group. --- Principal ideal domain. --- Principal ideal. --- Root of unity. --- Semigroup. --- Simplicial complex. --- Simply connected space. --- Special case. --- Square matrix. --- Subgroup. --- Subset. --- Summation. --- Theorem. --- Three-dimensional space (mathematics). --- Topological space. --- Topology. --- Torus knot. --- Transfinite number. --- Trefoil knot. --- Trichotomy (mathematics). --- Trivial group. --- Triviality (mathematics). --- Two-dimensional space. --- Unit vector. --- Wreath product.