Discrete group actions

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  • In this book I present differential geometry and related mathematical topics with the help of examples from physics. It is well known that there is something strikingly mathematical about the physical universe as it is conceived of in the physical sciences. The convergence of physics with mathematics, especially differential geometry, topology and global analysis is even more pronounced in the newer quantum theories such as gauge field theory and string theory. The amount of mathematical sophistication required for a good understanding of modern physics is astounding.

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  • We introduce a class of metric spaces which we call “bolic”. They include hyperbolic spaces, simply connected complete manifolds of nonpositive curvature, euclidean buildings, etc. We prove the Novikov conjecture on higher signatures for any discrete group which admits a proper isometric action on a “bolic”, weakly geodesic metric space of bounded geometry. 1. Introduction This work has grown out of an attempt to give a purely KK-theoretic proof of a result of A. Connes and H. Moscovici ([CM], [CGM]) that hyperbolic groups satisfy the Novikov conjecture. ...

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  • In the study of the theory of irreducible unitary representations, is necessary to analyze and demonstrate diverse results on integral orbital of functions belonging to the cohomology Hi (g, K; V  V*), and that it is wanted they belong to the L2(G)-cohomology of their reducible unitary representations called discrete series. Then is necessary consider the Frèchet space I(G), and analyze the 2-integrability to the fibers of the space G/K, in spaces or locally compact components of G/K.

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  • AC/DC I/O interface. A discrete interface that converts alternating current (AC) voltages from field devices into direct current (DC) signals that the processor can use. It can also convert DC signals into proportional AC voltages. action. A set of control instructions prompting a PLC to perform a certain control function during the execution of a sequential function chart step. acyclic message. An unscheduled message transmission. A/D. See analog-to-digital converter. address. (1) The location in a computer’s memory where particular information is stored.

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  • We prove the Bers density conjecture for singly degenerate Kleinian surface groups without parabolics. 1. Introduction In this paper we address a conjecture of Bers about singly degenerate Kleinian groups. These are discrete subgroups of PSL2 C that exhibit some unusual behavior: • As groups of projective transformations of the Riemann sphere C they act properly discontinuously on a topological disk whose closure is all of C. • As groups of hyperbolic isometries their action on H3 is not convex cocompact. ...

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