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The description for this book, Surface Area. (AM-35), Volume 35, will be forthcoming.

Surfaces. --- Absolute continuity. --- Addition. --- Admissible set. --- Arc length. --- Axiom. --- Axiomatic system. --- Bearing (navigation). --- Bounded variation. --- Calculus of variations. --- Circumference. --- Compact space. --- Complex analysis. --- Concentric. --- Connected space. --- Continuous function (set theory). --- Continuous function. --- Corollary. --- Countable set. --- Covering set. --- Curve. --- Derivative. --- Diameter. --- Differentiable function. --- Differential geometry. --- Direct proof. --- Dirichlet integral. --- Disjoint sets. --- Empty set. --- Equation. --- Equicontinuity. --- Existence theorem. --- Existential quantification. --- Function (mathematics). --- Functional analysis. --- Geometry. --- Hausdorff measure. --- Homeomorphism. --- Homotopy. --- Infimum and supremum. --- Integral geometry. --- Intersection number (graph theory). --- Interval (mathematics). --- Iterative method. --- Jacobian. --- Lebesgue integration. --- Lebesgue measure. --- Limit (mathematics). --- Limit point. --- Limit superior and limit inferior. --- Linearity. --- Line–line intersection. --- Locally compact space. --- Mathematician. --- Mathematics. --- Measure (mathematics). --- Metric space. --- Morphism. --- Natural number. --- Nonparametric statistics. --- Orientability. --- Parameter. --- Parametric equation. --- Parametric surface. --- Partial derivative. --- Potential theory. --- Radon–Nikodym theorem. --- Representation theorem. --- Representation theory. --- Right angle. --- Semi-continuity. --- Set function. --- Set theory. --- Sign (mathematics). --- Smoothness. --- Space-filling curve. --- Subset. --- Summation. --- Surface area. --- Tangent space. --- Theorem. --- Topological space. --- Topology. --- Total order. --- Total variation. --- Uniform convergence. --- Unit square.

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Study 79 contains a collection of papers presented at the Conference on Discontinuous Groups and Ricmann Surfaces at the University of Maryland, May 21-25, 1973. The papers, by leading authorities, deal mainly with Fuchsian and Kleinian groups, Teichmüller spaces, Jacobian varieties, and quasiconformal mappings. These topics are intertwined, representing a common meeting of algebra, geometry, and analysis.

Group theory --- Complex analysis --- Number theory --- RIEMANN SURFACES --- Discontinuous groups --- congresses --- Congresses --- Riemann surfaces --- Congresses. --- Groupes discontinus --- Combinatorial topology --- Functions of complex variables --- Surfaces, Riemann --- Functions --- Abelian variety. --- Adjunction (field theory). --- Affine space. --- Algebraic curve. --- Algebraic structure. --- Analytic function. --- Arithmetic genus. --- Automorphism. --- Bernhard Riemann. --- Boundary (topology). --- Cauchy sequence. --- Cauchy–Schwarz inequality. --- Cayley–Hamilton theorem. --- Closed geodesic. --- Combination. --- Commutative diagram. --- Commutator subgroup. --- Compact Riemann surface. --- Complex dimension. --- Complex manifold. --- Complex multiplication. --- Complex space. --- Complex torus. --- Congruence subgroup. --- Conjugacy class. --- Convex set. --- Cyclic group. --- Degeneracy (mathematics). --- Diagram (category theory). --- Diffeomorphism. --- Differential form. --- Dimension (vector space). --- Disjoint sets. --- E7 (mathematics). --- Endomorphism. --- Equation. --- Equivalence class. --- Euclidean space. --- Existence theorem. --- Existential quantification. --- Finite group. --- Finitely generated group. --- Fuchsian group. --- Fundamental domain. --- Fundamental lemma (Langlands program). --- Fundamental polygon. --- Galois extension. --- Holomorphic function. --- Homeomorphism. --- Homology (mathematics). --- Homomorphism. --- Hurwitz's theorem (number theory). --- Inclusion map. --- Inequality (mathematics). --- Inner automorphism. --- Intersection (set theory). --- Irreducibility (mathematics). --- Isomorphism class. --- Isomorphism theorem. --- Jacobian variety. --- Jordan curve theorem. --- Kleinian group. --- Limit point. --- Mapping class group. --- Metric space. --- Monodromy. --- Monomorphism. --- Möbius transformation. --- Non-Euclidean geometry. --- Orthogonal trajectory. --- Permutation. --- Polynomial. --- Power series. --- Projective variety. --- Quadratic differential. --- Quadric. --- Quasi-projective variety. --- Quasiconformal mapping. --- Quotient space (topology). --- Rectangle. --- Riemann mapping theorem. --- Riemann surface. --- Schwarzian derivative. --- Simply connected space. --- Simultaneous equations. --- Special case. --- Subgroup. --- Subsequence. --- Surjective function. --- Symmetric space. --- Tangent space. --- Teichmüller space. --- Theorem. --- Topological space. --- Topology. --- Uniqueness theorem. --- Unit disk. --- Variable (mathematics). --- Winding number. --- Word problem (mathematics). --- RIEMANN SURFACES - congresses --- Discontinuous groups - Congresses --- Geometrie algebrique --- Fonctions d'une variable complexe --- Surfaces de riemann

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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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This book presents a classification of all (complex)irreducible representations of a reductive group withconnected centre, over a finite field. To achieve this,the author uses etale intersection cohomology, anddetailed information on representations of Weylgroups.

512 --- Characters of groups --- Finite fields (Algebra) --- Finite groups --- Groups, Finite --- Group theory --- Modules (Algebra) --- Modular fields (Algebra) --- Algebra, Abstract --- Algebraic fields --- Galois theory --- Characters, Group --- Group characters --- Groups, Characters of --- Representations of groups --- Rings (Algebra) --- Algebra --- 512 Algebra --- Finite groups. --- Characters of groups. --- Addition. --- Algebra representation. --- Algebraic closure. --- Algebraic group. --- Algebraic variety. --- Algebraically closed field. --- Bijection. --- Borel subgroup. --- Cartan subalgebra. --- Character table. --- Character theory. --- Characteristic function (probability theory). --- Characteristic polynomial. --- Class function (algebra). --- Classical group. --- Coefficient. --- Cohomology with compact support. --- Cohomology. --- Combination. --- Complex number. --- Computation. --- Conjugacy class. --- Connected component (graph theory). --- Coxeter group. --- Cyclic group. --- Cyclotomic polynomial. --- David Kazhdan. --- Dense set. --- Derived category. --- Diagram (category theory). --- Dimension. --- Direct sum. --- Disjoint sets. --- Disjoint union. --- E6 (mathematics). --- Eigenvalues and eigenvectors. --- Endomorphism. --- Equivalence class. --- Equivalence relation. --- Existential quantification. --- Explicit formula. --- Explicit formulae (L-function). --- Fiber bundle. --- Finite field. --- Finite group. --- Fourier transform. --- Green's function. --- Group (mathematics). --- Group action. --- Group representation. --- Harish-Chandra. --- Hecke algebra. --- Identity element. --- Integer. --- Irreducible representation. --- Isomorphism class. --- Jordan decomposition. --- Line bundle. --- Linear combination. --- Local system. --- Mathematical induction. --- Maximal torus. --- Module (mathematics). --- Monodromy. --- Morphism. --- Orthonormal basis. --- P-adic number. --- Parametrization. --- Parity (mathematics). --- Partially ordered set. --- Perverse sheaf. --- Pointwise. --- Polynomial. --- Quantity. --- Rational point. --- Reductive group. --- Ree group. --- Schubert variety. --- Scientific notation. --- Semisimple Lie algebra. --- Sheaf (mathematics). --- Simple group. --- Simple module. --- Special case. --- Standard basis. --- Subset. --- Subtraction. --- Summation. --- Surjective function. --- Symmetric group. --- Tensor product. --- Theorem. --- Two-dimensional space. --- Unipotent representation. --- Vector bundle. --- Vector space. --- Verma module. --- Weil conjecture. --- Weyl group. --- Zariski topology.

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This volume studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. This subject is large and rapidly growing. These lectures are intended to introduce some key ideas in the field, and to form a basis for further study. The reader is assumed to be familiar with the rudiments of complex variable theory and of two-dimensional differential geometry, as well as some basic topics from topology. This third edition contains a number of minor additions and improvements: A historical survey has been added, the definition of Lattés map has been made more inclusive, and the écalle-Voronin theory of parabolic points is described. The résidu itératif is studied, and the material on two complex variables has been expanded. Recent results on effective computability have been added, and the references have been expanded and updated. Written in his usual brilliant style, the author makes difficult mathematics look easy. This book is a very accessible source for much of what has been accomplished in the field.

Functions of complex variables --- Holomorphic mappings --- Riemann surfaces --- Fonctions d'une variable complexe --- Applications holomorphes --- Riemann, surfaces de --- Holomorphic mappings. --- Mappings, Holomorphic --- Functions of complex variables. --- Riemann surfaces. --- Surfaces, Riemann --- Functions --- Functions of several complex variables --- Mappings (Mathematics) --- Complex variables --- Elliptic functions --- Functions of real variables --- Absolute value. --- Addition. --- Algebraic equation. --- Attractor. --- Automorphism. --- Beltrami equation. --- Blaschke product. --- Boundary (topology). --- Branched covering. --- Coefficient. --- Compact Riemann surface. --- Compact space. --- Complex analysis. --- Complex number. --- Complex plane. --- Computation. --- Connected component (graph theory). --- Connected space. --- Constant function. --- Continued fraction. --- Continuous function. --- Coordinate system. --- Corollary. --- Covering space. --- Cross-ratio. --- Derivative. --- Diagram (category theory). --- Diameter. --- Diffeomorphism. --- Differentiable manifold. --- Disjoint sets. --- Disjoint union. --- Disk (mathematics). --- Division by zero. --- Equation. --- Euler characteristic. --- Existential quantification. --- Exponential map (Lie theory). --- Fundamental group. --- Harmonic function. --- Holomorphic function. --- Homeomorphism. --- Hyperbolic geometry. --- Inequality (mathematics). --- Integer. --- Inverse function. --- Irrational rotation. --- Iteration. --- Jordan curve theorem. --- Julia set. --- Lebesgue measure. --- Lecture. --- Limit point. --- Line segment. --- Linear map. --- Linearization. --- Mandelbrot set. --- Mathematical analysis. --- Maximum modulus principle. --- Metric space. --- Monotonic function. --- Montel's theorem. --- Normal family. --- Open set. --- Orbifold. --- Parameter space. --- Parameter. --- Periodic point. --- Point at infinity. --- Polynomial. --- Power series. --- Proper map. --- Quadratic function. --- Rational approximation. --- Rational function. --- Rational number. --- Real number. --- Riemann sphere. --- Riemann surface. --- Root of unity. --- Rotation number. --- Schwarz lemma. --- Scientific notation. --- Sequence. --- Simply connected space. --- Special case. --- Subgroup. --- Subsequence. --- Subset. --- Summation. --- Tangent space. --- Theorem. --- Topological space. --- Topology. --- Uniform convergence. --- Uniformization theorem. --- Unit circle. --- Unit disk. --- Upper half-plane. --- Winding number.