Download E-books Group Acting on Hyperbolic Space. : Harmonic Analysis and Number Theory PDF

By Fritz Grunewald, Jens Mennicke

This e-book is anxious with discontinuous teams of motions of the original attached and easily attached Riemannian 3-manifold of continuous curva­ ture -1, that is typically known as hyperbolic 3-space. This house is the three-dimensional example of a similar Riemannian manifold which exists uniquely in each size n :::: 2. The hyperbolic areas seemed first within the paintings of Lobachevski within the first half the nineteenth century. Very early within the final century the gang of isometries of those areas was once studied through Steiner, while he checked out the crowd generated by way of the inversions in spheres. The ge­ ometries underlying the hyperbolic areas have been of primary significance in view that Lobachevski, Bolyai and Gauß had saw that they don't fulfill the axiom of parallels. Already within the classical works a number of concrete coordinate versions of hy­ perbolic 3-space have seemed. They make particular computations attainable and likewise supply identifications of the total staff of motions or isometries with famous matrix teams. One such version, because of H. Poincare, is the higher three half-space IH in JR . the gang of isometries is then pointed out with an exten­ sion of index 2 of the crowd PSL(2,

Show description

Read or Download Group Acting on Hyperbolic Space. : Harmonic Analysis and Number Theory PDF

Similar Abstract books

Lectures in Abstract Algebra, Part 3: Theory of Fields and Galois Theory (Graduate Texts in Mathematics 32)

The current quantity completes the sequence of texts on algebra which the writer begun greater than ten years in the past. The account of box concept and Galois idea which we provide this is in response to the notions and result of basic algebra which look in our first quantity and at the extra trouble-free elements of the second one quantity, facing linear algebra.

Measure and Category: A Survey of the Analogies between Topological and Measure Spaces (Graduate Texts in Mathematics)

During this version, a collection of Supplementary Notes and comments has been additional on the finish, grouped in keeping with bankruptcy. a few of these name awareness to next advancements, others upload extra clarification or extra comments. many of the comments are observed via a in short indicated evidence, that's occasionally varied from the single given within the reference brought up.

Cohomology of Groups (Graduate Texts in Mathematics, No. 87)

Geared toward moment 12 months graduate scholars, this article introduces them to cohomology conception (involving a wealthy interaction among algebra and topology) with no less than necessities. No homological algebra is believed past what's more often than not discovered in a primary path in algebraic topology, and the fundamentals of the topic, in addition to routines, are given sooner than dialogue of extra really good issues.

Permutation Groups (Graduate Texts in Mathematics)

Following the elemental principles, usual structures and demanding examples within the conception of permutation teams, the e-book is going directly to boost the combinatorial and workforce theoretic constitution of primitive teams resulting in the facts of the pivotal ONan-Scott Theorem which hyperlinks finite primitive teams with finite easy teams.

Extra info for Group Acting on Hyperbolic Space. : Harmonic Analysis and Number Theory

Show sample text content

Rated 4.82 of 5 – based on 14 votes