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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 Appendices provide a full discussion of the classification of homotopy tori, including Casson's unpublished work and a consideration of periodicity in topological surgery.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

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The theory of Riemann surfaces has a geometric and an analytic part. The former deals with the axiomatic definition of a Riemann surface, methods of construction, topological equivalence, and conformal mappings of one Riemann surface on another. The analytic part is concerned with the existence and properties of functions that have a special character connected with the conformal structure, for instance: subharmonic, harmonic, and analytic functions.Originally published in 1960.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.

515.16 --- 515.16 Topology of manifolds --- Topology of manifolds --- Riemann surfaces. --- Topology. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Surfaces, Riemann --- Functions --- Analytic function. --- Axiom of choice. --- Basis (linear algebra). --- Betti number. --- Big O notation. --- Bijection. --- Bilinear form. --- Bolzano–Weierstrass theorem. --- Boundary (topology). --- Boundary value problem. --- Bounded set (topological vector space). --- Branch point. --- Canonical basis. --- Cauchy sequence. --- Cauchy's integral formula. --- Characterization (mathematics). --- Coefficient. --- Commutator subgroup. --- Compact space. --- Compactification (mathematics). --- Conformal map. --- Connected space. --- Connectedness. --- Continuous function (set theory). --- Continuous function. --- Coset. --- Cross-cap. --- Dirichlet integral. --- Disjoint union. --- Elementary function. --- Elliptic surface. --- Exact differential. --- Existence theorem. --- Existential quantification. --- Extremal length. --- Family of sets. --- Finite intersection property. --- Finitely generated abelian group. --- Free group. --- Function (mathematics). --- Fundamental group. --- Green's function. --- Harmonic differential. --- Harmonic function. --- Harmonic measure. --- Heine–Borel theorem. --- Homeomorphism. --- Homology (mathematics). --- Ideal point. --- Infimum and supremum. --- Isolated point. --- Isolated singularity. --- Jordan curve theorem. --- Lebesgue integration. --- Limit point. --- Line segment. --- Linear independence. --- Linear map. --- Maximal set. --- Maximum principle. --- Meromorphic function. --- Metric space. --- Normal operator. --- Normal subgroup. --- Open set. --- Orientability. --- Orthogonal complement. --- Partition of unity. --- Point at infinity. --- Polyhedron. --- Positive harmonic function. --- Principal value. --- Projection (linear algebra). --- Projection (mathematics). --- Removable singularity. --- Riemann mapping theorem. --- Riemann surface. --- Semi-continuity. --- Sign (mathematics). --- Simplicial homology. --- Simply connected space. --- Singular homology. --- Skew-symmetric matrix. --- Special case. --- Subgroup. --- Subset. --- Summation. --- Support (mathematics). --- Taylor series. --- Theorem. --- Topological space. --- Triangle inequality. --- Uniform continuity. --- Uniformization theorem. --- Unit disk. --- Upper and lower bounds. --- Upper half-plane. --- Weyl's lemma (Laplace equation). --- Zorn's lemma.