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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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Group theory and topology are closely related. The region of their interaction, combining the logical clarity of algebra with the depths of geometric intuition, is the subject of Combinatorial Group Theory and Topology. The work includes papers from a conference held in July 1984 at Alta Lodge, Utah.Contributors to the book include Roger Alperin, Hyman Bass, Max Benson, Joan S. Birman, Andrew J. Casson, Marshall Cohen, Donald J. Collins, Robert Craggs, Michael Dyer, Beno Eckmann, Stephen M. Gersten, Jane Gilman, Robert H. Gilman, Narain D. Gupta, John Hempel, James Howie, Roger Lyndon, Martin Lustig, Lee P. Neuwirth, Andrew J. Nicas, N. Patterson, John G. Ratcliffe, Frank Rimlinger, Caroline Series, John R. Stallings, C. W. Stark, and A. Royce Wolf.

Combinatorial group theory --- Topology --- Abelian group. --- Algebraic equation. --- Algebraic integer. --- Automorphism. --- Basis (linear algebra). --- Betti number. --- Cayley graph. --- Cayley–Hamilton theorem. --- Characteristic polynomial. --- Characteristic subgroup. --- Characterization (mathematics). --- Classifying space. --- Combinatorial group theory. --- Combinatorics. --- Commutative algebra. --- Commutative property. --- Commutator subgroup. --- Compactification (mathematics). --- Complement (set theory). --- Conformal map. --- Conjugacy class. --- Connected component (graph theory). --- Connectivity (graph theory). --- Coprime integers. --- Coset. --- Coxeter group. --- Cyclic group. --- Cyclic permutation. --- Degeneracy (mathematics). --- Dehn's lemma. --- Diagram (category theory). --- Dirac delta function. --- Disk (mathematics). --- Epimorphism. --- Equation. --- Euclidean group. --- Finite group. --- Finitely generated abelian group. --- Finitely generated group. --- Free abelian group. --- Free group. --- Freiheitssatz. --- Fuchsian group. --- Function (mathematics). --- Fundamental domain. --- Fundamental group. --- Fundamental lemma (Langlands program). --- G-module. --- General linear group. --- Generating set of a group. --- Geodesic. --- Graph (discrete mathematics). --- Graph of groups. --- Graph product. --- Group theory. --- Haken manifold. --- Harmonic analysis. --- Homological algebra. --- Homology (mathematics). --- Homomorphism. --- Homotopy. --- Hurwitz's theorem (number theory). --- Hyperbolic 3-manifold. --- Identity theorem. --- Inclusion map. --- Inequality (mathematics). --- Inner automorphism. --- Intersection (set theory). --- Intersection number (graph theory). --- Intersection number. --- Invertible matrix. --- Jacobian matrix and determinant. --- Knot theory. --- Limit point. --- Mapping class group. --- Mapping cone (homological algebra). --- Mathematical induction. --- Module (mathematics). --- Parity (mathematics). --- Poincaré conjecture. --- Prime number. --- Pullback (category theory). --- Quotient group. --- Representation theory. --- Residually finite group. --- Riemann surface. --- Seifert–van Kampen theorem. --- Separatrix (mathematics). --- Set theory. --- Simplicial complex. --- Sphere theorem (3-manifolds). --- Sphere theorem. --- Subgroup. --- Sylow theorems. --- Theorem. --- Topology. --- Union (set theory). --- Uniqueness theorem. --- Variable (mathematics). --- Word problem (mathematics).