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Groups Acting on Hyperbolic Space
This book is concerned with discontinuous groups of motions of the unique connected and simply connected Riemannian 3-manifold of constant curva ture -1, which is traditionally called hyperbolic 3-space. This space is the 3-dimensional instance of an analogous Riemannian manifold which exists uniquely in every dimension n :::: 2. The hyperbolic spaces appeared first in the work of Lobachevski in the first half of the 19th century. Very early in the last century the group of isometries of these spaces was studied by Steiner, when he looked at the group generated by the inversions in spheres. The ge ometries underlying the hyperbolic spaces were of fundamental importance since Lobachevski, Bolyai and Gauß had observed that they do not satisfy the axiom of parallels. Already in the classical works several concrete coordinate models of hy perbolic 3-space have appeared. They make explicit computations possible and also give identifications of the full group of motions or isometries with well-known matrix groups. One such model, due to H. Poincare, is the upper 3 half-space IH in JR . The group of isometries is then identified with an exten sion of index 2 of the group PSL(2,
Group Theory
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Conformal Geometry of Discrete Groups and Manifolds
The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, Univ...
Dynamics of Discrete Group Action
Provides the first systematic study of geometry and topology of locally symmetric rank one manifolds and dynamics of discrete action of their fundamental groups. In addition to geometry and topology, this study involves several other areas of Mathematics – from algebra of varieties of groups representations and geometric group theory, to geometric analysis including classical questions from function theory.
Analytic Number Theory
Articles in this volume are based on talks given at the Gauss-Dirichlet Conference held in Gottingen on June 20-24, 2005. The conference commemorated the 150th anniversary of the death of C.-F. Gauss and the 200th anniversary of the birth of J.-L. Dirichlet. The volume begins with a definitive summary of the life and work of Dirichlet and continues with thirteen papers by leading experts on research topics of current interest in number theory that were directly influenced by Gauss and Dirichlet. Among the topics are the distribution of primes (long arithmetic progressions of primes and small gaps between primes), class groups of binary quadratic forms, various aspects of the theory of $L$-functions, the theory of modular forms, and the study of rational and integral solutions to polynomial equations in several variables. Information for our distributors: Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).
Geometric and Computational Perspectives on Infinite Groups
This book contains the proceedings of two workshops on computational aspects of geometric group theory.
Word Problems
Word Problems
Direction of Time
This edited book presents the problems of time and direction from an interdisciplinary point of view, concentrating in particular on the following relations: • Time and physics • Time, philosophy and psychology • Time, mathematics and information theory It is a unique contribution by philosophers and scientists who are active in mathematics, physics, biology, engineering, information theory and psychology. Questions such as the existence of a Big Bang, the neurobiological basis regarding the coexistence of free will and determinism, intercultural aspects of time, mathematical models of time, psychopathological features of time, and micro reversibility versus macroscopic irreversibility are studied. It also provides a truly interdisciplinary study of the problematic 'arrow of time'.
Computational Aspects of Discrete Subgroups of Lie Groups
This volume contains the proceedings of the virtual workshop on Computational Aspects of Discrete Subgroups of Lie Groups, held from June 14 to June 18, 2021, and hosted by the Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, Rhode Island. The major theme deals with a novel domain of computational algebra: the design, implementation, and application of algorithms based on matrix representation of groups and their geometric properties. It is centered on computing with discrete subgroups of Lie groups, which impacts many different areas of mathematics such as algebra, geometry, topology, and number theory. The workshop aimed to synergize independent strands in the area of computing with discrete subgroups of Lie groups, to facilitate solution of theoretical problems by means of recent advances in computational algebra.
Groups - Korea 1988
These proceedings include selected and refereed original papers; most are research papers, a few are comprehensive survey articles.
