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Part exposition and part presentation of new results, this monograph deals with that area of mathematics which has both combinatorial group theory and mathematical logic in common. Its main topics are the word problem for groups, the conjugacy problem for groups, and the isomorphism problem for groups. The presentation depends on previous results of J. L. Britton, which, with other factual background, are treated in detail.

Group theory --- 510.6 --- Mathematical logic --- 510.6 Mathematical logic --- Group theory. --- Logic, Symbolic and mathematical. --- Groupes, Théorie des --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Algebra of logic --- Logic, Universal --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Abelian group. --- Betti number. --- Characteristic function (probability theory). --- Characterization (mathematics). --- Combinatorial group theory. --- Conjecture. --- Conjugacy class. --- Conjugacy problem. --- Contradiction. --- Corollary. --- Cyclic permutation. --- Decision problem. --- Diffeomorphism. --- Direct product. --- Direct proof. --- Effective method. --- Elementary class. --- Embedding. --- Enumeration. --- Epimorphism. --- Equation. --- Equivalence relation. --- Exact sequence. --- Existential quantification. --- Finite group. --- Finite set. --- Finitely generated group. --- Finitely presented. --- Free group. --- Free product. --- Fundamental group. --- Fundamental theorem. --- Group (mathematics). --- Gödel numbering. --- Homomorphism. --- Homotopy. --- Inner automorphism. --- Markov property. --- Mathematical logic. --- Mathematical proof. --- Mathematics. --- Monograph. --- Natural number. --- Nilpotent group. --- Normal subgroup. --- Notation. --- Permutation. --- Polycyclic group. --- Presentation of a group. --- Quotient group. --- Recursive set. --- Requirement. --- Residually finite group. --- Semigroup. --- Simple set. --- Simplicial complex. --- Solvable group. --- Statistical hypothesis testing. --- Subgroup. --- Theorem. --- Theory. --- Topology. --- Transitive relation. --- Triviality (mathematics). --- Truth table. --- Turing degree. --- Turing machine. --- Without loss of generality. --- Word problem (mathematics). --- Groupes, Théorie des --- Décidabilité (logique mathématique)

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The intention of the authors is to examine the relationship between piecewise linear structure and differential structure: a relationship, they assert, that can be understood as a homotopy obstruction theory, and, hence, can be studied by using the traditional techniques of algebraic topology.Thus the book attacks the problem of existence and classification (up to isotopy) of differential structures compatible with a given combinatorial structure on a manifold. The problem is completely "solved" in the sense that it is reduced to standard problems of algebraic topology.The first part of the book is purely geometrical; it proves that every smoothing of the product of a manifold M and an interval is derived from an essentially unique smoothing of M. In the second part this result is used to translate the classification of smoothings into the problem of putting a linear structure on the tangent microbundle of M. This in turn is converted to the homotopy problem of classifying maps from M into a certain space PL/O. The set of equivalence classes of smoothings on M is given a natural abelian group structure.

Algebraic topology --- Piecewise linear topology --- Manifolds (Mathematics) --- Topologie linéaire par morceaux --- Variétés (Mathématiques) --- 515.16 --- PL topology --- Topology --- Geometry, Differential --- Topology of manifolds --- Piecewise linear topology. --- Manifolds (Mathematics). --- 515.16 Topology of manifolds --- Topologie linéaire par morceaux --- Variétés (Mathématiques) --- Affine transformation. --- Approximation. --- Associative property. --- Bijection. --- Bundle map. --- Classification theorem. --- Codimension. --- Coefficient. --- Cohomology. --- Commutative property. --- Computation. --- Convex cone. --- Convolution. --- Corollary. --- Counterexample. --- Diffeomorphism. --- Differentiable function. --- Differentiable manifold. --- Differential structure. --- Dimension. --- Direct proof. --- Division by zero. --- Embedding. --- Empty set. --- Equivalence class. --- Equivalence relation. --- Euclidean space. --- Existential quantification. --- Exponential map (Lie theory). --- Fiber bundle. --- Fibration. --- Functor. --- Grassmannian. --- H-space. --- Homeomorphism. --- Homotopy. --- Integral curve. --- Inverse problem. --- Isomorphism class. --- K0. --- Linearization. --- Manifold. --- Mathematical induction. --- Milnor conjecture. --- Natural transformation. --- Neighbourhood (mathematics). --- Normal bundle. --- Obstruction theory. --- Open set. --- Partition of unity. --- Piecewise linear. --- Polyhedron. --- Reflexive relation. --- Regular map (graph theory). --- Sheaf (mathematics). --- Smoothing. --- Smoothness. --- Special case. --- Submanifold. --- Tangent bundle. --- Tangent vector. --- Theorem. --- Topological manifold. --- Topological space. --- Topology. --- Transition function. --- Transitive relation. --- Vector bundle. --- Vector field. --- Variétés topologiques

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Written by Arthur Ogus on the basis of notes from Pierre Berthelot's seminar on crystalline cohomology at Princeton University in the spring of 1974, this book constitutes an informal introduction to a significant branch of algebraic geometry. Specifically, it provides the basic tools used in the study of crystalline cohomology of algebraic varieties in positive characteristic.Originally published in 1978.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.

Algebraic geometry --- Geometry, Algebraic. --- Homology theory. --- Functions, Zeta. --- Zeta functions --- Cohomology theory --- Contrahomology theory --- Algebraic topology --- Geometry --- Abelian category. --- Additive map. --- Adjoint functors. --- Adjunction (field theory). --- Adjunction formula. --- Alexander Grothendieck. --- Algebra homomorphism. --- Artinian. --- Automorphism. --- Axiom. --- Banach space. --- Base change map. --- Base change. --- Betti number. --- Calculation. --- Cartesian product. --- Category of abelian groups. --- Characteristic polynomial. --- Characterization (mathematics). --- Closed immersion. --- Codimension. --- Coefficient. --- Cohomology. --- Cokernel. --- Commutative diagram. --- Commutative property. --- Commutative ring. --- Compact space. --- Corollary. --- Crystalline cohomology. --- De Rham cohomology. --- Degeneracy (mathematics). --- Derived category. --- Diagram (category theory). --- Differential operator. --- Discrete valuation ring. --- Divisibility rule. --- Dual basis. --- Eigenvalues and eigenvectors. --- Endomorphism. --- Epimorphism. --- Equation. --- Equivalence of categories. --- Exact sequence. --- Existential quantification. --- Explicit formula. --- Explicit formulae (L-function). --- Exponential type. --- Exterior algebra. --- Exterior derivative. --- Formal power series. --- Formal scheme. --- Frobenius endomorphism. --- Functor. --- Fundamental theorem. --- Hasse invariant. --- Hodge theory. --- Homotopy. --- Ideal (ring theory). --- Initial and terminal objects. --- Inverse image functor. --- Inverse limit. --- Inverse system. --- K-theory. --- Leray spectral sequence. --- Linear map. --- Linearization. --- Locally constant function. --- Mapping cone (homological algebra). --- Mathematical induction. --- Maximal ideal. --- Module (mathematics). --- Monomial. --- Monotonic function. --- Morphism. --- Natural transformation. --- Newton polygon. --- Noetherian ring. --- Noetherian. --- P-adic number. --- Polynomial. --- Power series. --- Presheaf (category theory). --- Projective module. --- Scientific notation. --- Series (mathematics). --- Sheaf (mathematics). --- Sheaf of modules. --- Special case. --- Spectral sequence. --- Subring. --- Subset. --- Symmetric algebra. --- Theorem. --- Topological space. --- Topology. --- Topos. --- Transitive relation. --- Universal property. --- Zariski topology. --- Geometrie algebrique --- Topologie algebrique --- Varietes algebriques --- Cohomologie

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The purpose of this book is to provide a self-contained account, accessible to the non-specialist, of algebra necessary for the solution of the integrability problem for transitive pseudogroup structures.Originally published in 1981.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.

Lie algebras. --- Ideals (Algebra) --- Pseudogroups. --- Global analysis (Mathematics) --- Lie groups --- Algebraic ideals --- Algebraic fields --- Rings (Algebra) --- Algebras, Lie --- Algebra, Abstract --- Algebras, Linear --- Lie algebras --- Pseudogroups --- 512.81 --- 512.81 Lie groups --- Ideals (Algebra). --- Lie, Algèbres de. --- Idéaux (algèbre) --- Pseudogroupes (mathématiques) --- Ordered algebraic structures --- Analytical spaces --- Addition. --- Adjoint representation. --- Algebra homomorphism. --- Algebra over a field. --- Algebraic extension. --- Algebraic structure. --- Analytic function. --- Associative algebra. --- Automorphism. --- Bilinear form. --- Bilinear map. --- Cartesian product. --- Closed graph theorem. --- Codimension. --- Coefficient. --- Cohomology. --- Commutative ring. --- Commutator. --- Compact space. --- Complex conjugate. --- Complexification (Lie group). --- Complexification. --- Conjecture. --- Constant term. --- Continuous function. --- Contradiction. --- Corollary. --- Counterexample. --- Diagram (category theory). --- Differentiable manifold. --- Differential form. --- Differential operator. --- Dimension (vector space). --- Dimension. --- Direct sum. --- Discrete space. --- Donald C. Spencer. --- Dual basis. --- Embedding. --- Epimorphism. --- Existential quantification. --- Exterior (topology). --- Exterior algebra. --- Exterior derivative. --- Faithful representation. --- Formal power series. --- Graded Lie algebra. --- Ground field. --- Homeomorphism. --- Homomorphism. --- Hyperplane. --- I0. --- Indeterminate (variable). --- Infinitesimal transformation. --- Injective function. --- Integer. --- Integral domain. --- Invariant subspace. --- Invariant theory. --- Isotropy. --- Jacobi identity. --- Levi decomposition. --- Lie algebra. --- Linear algebra. --- Linear map. --- Linear subspace. --- Local diffeomorphism. --- Mathematical induction. --- Maximal ideal. --- Module (mathematics). --- Monomorphism. --- Morphism. --- Natural transformation. --- Non-abelian. --- Partial differential equation. --- Pseudogroup. --- Pullback (category theory). --- Simple Lie group. --- Space form. --- Special case. --- Subalgebra. --- Submanifold. --- Subring. --- Summation. --- Symmetric algebra. --- Symplectic vector space. --- Telescoping series. --- Theorem. --- Topological algebra. --- Topological space. --- Topological vector space. --- Topology. --- Transitive relation. --- Triviality (mathematics). --- Unit vector. --- Universal enveloping algebra. --- Vector bundle. --- Vector field. --- Vector space. --- Weak topology. --- Lie, Algèbres de. --- Idéaux (algèbre) --- Pseudogroupes (mathématiques)

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Based on a series of lectures given by Harish-Chandra at the Institute for Advanced Study in 1971-1973, this book provides an introduction to the theory of harmonic analysis on reductive p-adic groups.Originally published in 1979.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.

512.74 --- p-adic groups --- Banach algebras --- Groups, p-adic --- Algebraic groups. Abelian varieties --- p-adic groups. --- 512.74 Algebraic groups. Abelian varieties --- P-adic groups. --- Harmonic analysis. Fourier analysis --- Harmonic analysis --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Group theory --- Harmonic analysis. --- Adjoint representation. --- Admissible representation. --- Algebra homomorphism. --- Algebraic group. --- Analytic continuation. --- Analytic function. --- Associative property. --- Automorphic form. --- Automorphism. --- Banach space. --- Bijection. --- Bilinear form. --- Borel subgroup. --- Cartan subgroup. --- Central simple algebra. --- Characteristic function (probability theory). --- Characterization (mathematics). --- Class function (algebra). --- Commutative property. --- Compact space. --- Composition series. --- Conjugacy class. --- Corollary. --- Dimension (vector space). --- Discrete series representation. --- Division algebra. --- Double coset. --- Eigenvalues and eigenvectors. --- Endomorphism. --- Epimorphism. --- Equivalence class. --- Equivalence relation. --- Existential quantification. --- Factorization. --- Fourier series. --- Function (mathematics). --- Functional equation. --- Fundamental domain. --- Fundamental lemma (Langlands program). --- G-module. --- Group isomorphism. --- Haar measure. --- Hecke algebra. --- Holomorphic function. --- Identity element. --- Induced representation. --- Inner automorphism. --- Lebesgue measure. --- Levi decomposition. --- Lie algebra. --- Locally constant function. --- Locally integrable function. --- Mathematical induction. --- Matrix coefficient. --- Maximal compact subgroup. --- Meromorphic function. --- Module (mathematics). --- Module homomorphism. --- Open set. --- Order of integration (calculus). --- Orthogonal complement. --- P-adic number. --- Pole (complex analysis). --- Product measure. --- Projection (linear algebra). --- Quotient module. --- Quotient space (topology). --- Radon measure. --- Reductive group. --- Representation of a Lie group. --- Representation theorem. --- Representation theory. --- Ring homomorphism. --- Schwartz space. --- Semisimple algebra. --- Separable extension. --- Sesquilinear form. --- Set (mathematics). --- Sign (mathematics). --- Square-integrable function. --- Sub"ient. --- Subalgebra. --- Subgroup. --- Subset. --- Summation. --- Support (mathematics). --- Surjective function. --- Tempered representation. --- Tensor product. --- Theorem. --- Topological group. --- Topological space. --- Topology. --- Trace (linear algebra). --- Transitive relation. --- Unitary representation. --- Universal enveloping algebra. --- Variable (mathematics). --- Vector space. --- Analyse harmonique (mathématiques)