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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.

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Fibre bundles, now an integral part of differential geometry, are also of great importance in modern physics--such as in gauge theory. This book, a succinct introduction to the subject by renown mathematician Norman Steenrod, was the first to present the subject systematically. It begins with a general introduction to bundles, including such topics as differentiable manifolds and covering spaces. The author then provides brief surveys of advanced topics, such as homotopy theory and cohomology theory, before using them to study further properties of fibre bundles. The result is a classic and timeless work of great utility that will appeal to serious mathematicians and theoretical physicists alike.

#WWIS:d.d. Prof. L. Bouckaert/ALTO --- 515.1 --- 515.1 Topology --- Topology --- Topology. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Algebraic topology. --- Associated bundle. --- Associative algebra. --- Associative property. --- Atlas (topology). --- Automorphism. --- Axiomatic system. --- Barycentric subdivision. --- Bilinear map. --- Bundle map. --- Classification theorem. --- Coefficient. --- Cohomology ring. --- Cohomology. --- Conjugacy class. --- Connected component (graph theory). --- Connected space. --- Coordinate system. --- Coset. --- Cup product. --- Cyclic group. --- Determinant. --- Differentiable manifold. --- Differential structure. --- Dimension (vector space). --- Direct product. --- Division algebra. --- Equivalence class. --- Equivalence relation. --- Euler number. --- Existence theorem. --- Existential quantification. --- Factorization. --- Fiber bundle. --- Frenet–Serret formulas. --- Gram–Schmidt process. --- Group theory. --- Homeomorphism. --- Homology (mathematics). --- Homomorphism. --- Homotopy group. --- Homotopy. --- Hopf theorem. --- Hurewicz theorem. --- Identity element. --- Inclusion map. --- Inner automorphism. --- Invariant subspace. --- Invertible matrix. --- Jacobian matrix and determinant. --- Klein bottle. --- Lattice of subgroups. --- Lie group. --- Line element. --- Line segment. --- Linear map. --- Linear space (geometry). --- Linear subspace. --- Manifold. --- Mapping cylinder. --- Metric tensor. --- N-sphere. --- Natural topology. --- Octonion. --- Open set. --- Orientability. --- Orthogonal group. --- Orthogonalization. --- Permutation. --- Principal bundle. --- Product topology. --- Quadratic form. --- Quaternion. --- Retract. --- Separable space. --- Set theory. --- Simplicial complex. --- Special case. --- Stiefel manifold. --- Subalgebra. --- Subbase. --- Subgroup. --- Subset. --- Symmetric tensor. --- Tangent bundle. --- Tangent space. --- Tangent vector. --- Tensor field. --- Tensor. --- Theorem. --- Tietze extension theorem. --- Topological group. --- Topological space. --- Transitive relation. --- Transpose. --- Union (set theory). --- Unit sphere. --- Universal bundle. --- Vector field.

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The central theme of this study is Artin's braid group and the many ways that the notion of a braid has proved to be important in low-dimensional topology.In Chapter 1 the author is concerned with the concept of a braid as a group of motions of points in a manifold. She studies structural and algebraic properties of the braid groups of two manifolds, and derives systems of defining relations for the braid groups of the plane and sphere. In Chapter 2 she focuses on the connections between the classical braid group and the classical knot problem. After reviewing basic results she proceeds to an exploration of some possible implications of the Garside and Markov theorems.Chapter 3 offers discussion of matrix representations of the free group and of subgroups of the automorphism group of the free group. These ideas come to a focus in the difficult open question of whether Burau's matrix representation of the braid group is faithful. Chapter 4 is a broad view of recent results on the connections between braid groups and mapping class groups of surfaces. Chapter 5 contains a brief discussion of the theory of "plats." Research problems are included in an appendix.

Braid theory --- Braids, Theory of --- Theory of braids --- Braid theory. --- Algebraic topology --- Knot theory --- Representations of groups --- 512.54 --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Knots (Topology) --- Low-dimensional topology --- 512.54 Groups. Group theory --- Groups. Group theory --- Knot theory. --- Representations of groups. --- Addition. --- Alexander polynomial. --- Algebraic structure. --- Automorphism. --- Ball (mathematics). --- Bijection. --- Braid group. --- Branched covering. --- Burau representation. --- Calculation. --- Cartesian coordinate system. --- Characterization (mathematics). --- Coefficient. --- Combinatorial group theory. --- Commutative property. --- Commutator subgroup. --- Configuration space. --- Conjugacy class. --- Corollary. --- Covering space. --- Dehn twist. --- Determinant. --- Diagram (category theory). --- Dimension. --- Disjoint union. --- Double coset. --- Eigenvalues and eigenvectors. --- Enumeration. --- Equation. --- Equivalence class. --- Exact sequence. --- Existential quantification. --- Faithful representation. --- Finite set. --- Free abelian group. --- Free group. --- Fundamental group. --- Geometry. --- Group (mathematics). --- Group ring. --- Groupoid. --- Handlebody. --- Heegaard splitting. --- Homeomorphism. --- Homomorphism. --- Homotopy group. --- Homotopy. --- Identity element. --- Identity matrix. --- Inclusion map. --- Initial point. --- Integer matrix. --- Integer. --- Knot polynomial. --- Lens space. --- Line segment. --- Line–line intersection. --- Link group. --- Low-dimensional topology. --- Mapping class group. --- Mathematical induction. --- Mathematics. --- Matrix group. --- Matrix representation. --- Monograph. --- Morphism. --- Natural transformation. --- Normal matrix. --- Notation. --- Orientability. --- Parity (mathematics). --- Permutation. --- Piecewise linear. --- Pointwise. --- Polynomial. --- Prime knot. --- Projection (mathematics). --- Proportionality (mathematics). --- Quotient group. --- Requirement. --- Rewriting. --- Riemann surface. --- Semigroup. --- Sequence. --- Special case. --- Subgroup. --- Submanifold. --- Subset. --- Symmetric group. --- Theorem. --- Theory. --- Topology. --- Trefoil knot. --- Two-dimensional space. --- Unimodular matrix. --- Unit vector. --- Variable (mathematics). --- Word problem (mathematics). --- Topologie algébrique

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Book 4 in the Princeton Mathematical Series.Originally published in 1941.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.

Topology. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Abelian group. --- Additive group. --- Adjunction (field theory). --- Algebraic connectivity. --- Algebraic number. --- Annihilator (ring theory). --- Automorphism. --- Barycentric coordinate system. --- Barycentric subdivision. --- Big O notation. --- Boundary (topology). --- Cantor set. --- Cardinal number. --- Cartesian coordinate system. --- Cauchy sequence. --- Character group. --- Circumference. --- Cohomology. --- Combinatorics. --- Compact space. --- Complete metric space. --- Complex number. --- Computation. --- Continuous function (set theory). --- Continuous function. --- Contractible space. --- Cyclic group. --- Dense set. --- Diameter. --- Dimension (vector space). --- Dimension function. --- Dimension theory (algebra). --- Dimension. --- Dimensional analysis. --- Discrete group. --- Disjoint sets. --- Domain of a function. --- Equation. --- Euclidean space. --- Existential quantification. --- Exponentiation. --- Function (mathematics). --- Function space. --- Fundamental theorem. --- Geometry. --- Group theory. --- Hausdorff dimension. --- Hausdorff space. --- Hilbert cube. --- Hilbert space. --- Homeomorphism. --- Homology (mathematics). --- Homomorphism. --- Homotopy. --- Hyperplane. --- Integer. --- Interior (topology). --- Invariance of domain. --- Inverse system. --- Linear space (geometry). --- Linear subspace. --- Lp space. --- Mathematical induction. --- Mathematics. --- Metric space. --- Multiplicative group. --- N-sphere. --- Natural number. --- Natural transformation. --- Ordinal number. --- Orientability. --- Parity (mathematics). --- Partial function. --- Partially ordered set. --- Point (geometry). --- Polytope. --- Projection (linear algebra). --- Samuel Eilenberg. --- Separable space. --- Separated sets. --- Set (mathematics). --- Set theory. --- Sign (mathematics). --- Simplex. --- Special case. --- Subgroup. --- Subsequence. --- Subset. --- Summation. --- Theorem. --- Three-dimensional space (mathematics). --- Topological group. --- Topological property. --- Topological space. --- Transfinite. --- Transitive relation. --- Unit sphere. --- Upper and lower bounds. --- Variable (mathematics).

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Global analysis describes diverse yet interrelated research areas in analysis and algebraic geometry, particularly those in which Kunihiko Kodaira made his most outstanding contributions to mathematics. The eminent contributors to this volume, from Japan, the United States, and Europe, have prepared original research papers that illustrate the progress and direction of current research in complex variables and algebraic and differential geometry. The authors investigate, among other topics, complex manifolds, vector bundles, curved 4-dimensional space, and holomorphic mappings. Bibliographies facilitate further reading in the development of the various studies.Originally published in 1970.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 geometry. Global analysis --- Global analysis (Mathematics) --- Calculus of variations --- Differentiable manifolds --- 517.97 --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Calculus of variations. Mathematical theory of control --- Differentiable manifolds. --- Calculus of variations. --- Global analysis (Mathematics). --- 517.97 Calculus of variations. Mathematical theory of control --- Algebraic topology --- 514.7 --- -Calculus of variations --- #TCPW W3.0 --- #TCPW W3.2 --- #WWIS:MEET --- Differential manifolds --- Manifolds (Mathematics) --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Differential geometry. Algebraic and analytic methods in geometry --- 514.7 Differential geometry. Algebraic and analytic methods in geometry --- Addresses, essays, lectures --- Functional analysis --- Geometry --- Algebra homomorphism. --- Algebraic space. --- Associated graded ring. --- Automorphism. --- Betti number. --- Bilinear form. --- Canonical basis. --- Canonical bundle. --- Closed immersion. --- Codimension. --- Coefficient. --- Cohomology. --- Cokernel. --- Complete intersection. --- Complex manifold. --- Complex torus. --- Convex cone. --- Covering space. --- Dedekind domain. --- Deformation theory. --- Degenerate bilinear form. --- Diagram (category theory). --- Diffeomorphism. --- Differential form. --- Discrete group. --- Discrete valuation ring. --- Divisor. --- Elliptic operator. --- Elliptic surface. --- Endomorphism. --- Enriques surface. --- Epimorphism. --- Equation. --- Exact sequence. --- Existential quantification. --- Extremal length. --- Fiber bundle. --- Flat morphism. --- Frame bundle. --- Functor. --- Generic point. --- Grassmannian. --- Harmonic function. --- Heine–Borel theorem. --- Hensel's lemma. --- Holomorphic function. --- Homogeneous coordinates. --- Homomorphism. --- Hyperplane. --- Invertible sheaf. --- Kodaira embedding theorem. --- Kodaira vanishing theorem. --- Lie algebra. --- Line bundle. --- Linear independence. --- Linear map. --- Local ring. --- Mathematical induction. --- Meromorphic function. --- Metric space. --- Morphism. --- Natural number. --- Norm (mathematics). --- Normal extension. --- Normal subgroup. --- Open set. --- Orientability. --- Orthonormal basis. --- Partition of unity. --- Polynomial. --- Principal bundle. --- Principal homogeneous space. --- Projection (mathematics). --- Projective line. --- Quadric. --- Rational singularity. --- Residue field. --- Riemannian manifold. --- Ring homomorphism. --- Self-adjoint operator. --- Sheaf (mathematics). --- Sobolev space. --- Special case. --- Stokes' theorem. --- Subgroup. --- Submanifold. --- Subset. --- Subspace theorem. --- Summation. --- Surjective function. --- Symmetric tensor. --- Symplectic vector space. --- Tangent space. --- Theorem. --- Universal bundle. --- Upper and lower bounds. --- Vector bundle. --- Vector field. --- Wirtinger inequality (2-forms). --- Zariski topology. --- Analyse globale (mathématiques) --- Calcul des variations --- Analyse globale (mathématiques) --- Kodaira (kunihiko), mathematicien japonais, 1915 --- -Kodaira (kunihiko), mathematicien japonais, 1915 --- -517.97 --- -Analyse globale (mathématiques) --- -Algebraic topology