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# ðŸ“™ Classical Aspherical Manifolds by F. Thomas Farrell and L. Edwin Jones â€” download pdf

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Aspherical manifolds--those whose universal covers are contractible--arise classically in many areas of mathematics. They occur in Lie group theory as certain double coset spaces and in synthetic geometry as the space forms preserving the geometry. This volume contains lectures delivered by the first author at an NSF-CBMS Regional Conference on K-Theory and Dynamics, held in Gainesville, Florida in January, 1989. The lectures were primarily concerned with the problem of topologically characterizing classical aspherical manifolds. This problem has for the most part been solved, but the 3- and 4-dimensional cases remain the most important open questions; Poincare's conjecture is closely related to the 3-dimensional problem. One of the main results is that a closed aspherical manifold (of dimension $\neq$ 3 or 4) is a hyperbolic space if and only if its fundamental group is isomorphic to a discrete, cocompact subgroup of the Lie group $O(n,1;{\mathbb R})$. One of the book's themes is how the dynamics of the geodesic flow can be combined with topological control theory to study properly discontinuous group actions on $R^n$. Some of the more technical topics of the lectures have been deleted, and some additional results obtained since the conference are discussed in an epilogue. The book requires some familiarity with the material contained in a basic, graduate-level course in algebraic and differential topology, as well as some elementary differential geometry.

## About book:

## About file:

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- Series:
**Regional conference series in mathematics 75** - Author:
**F. Thomas Farrell and L. Edwin Jones** - Year:
**1990** - Publisher:
**Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society** - Language:
**English** - ISBN:
**9780821807262,0821807269**

- File size:
**1 999 109** - Format:
**djvu**

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The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of r...

The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of r...

Seifert fiberings extend the notion of fiber bundle mappings by allowing some of the fibers to be singular. Away from the singular fibers, the fibering is an ordinary bundle with fiber a fixed homogeneous space. The singular fibers are quotients of this h...

Fourier Integrals in Classical Analysis is an advanced monograph concerned with modern treatments of central problems in harmonic analysis. The main theme of the book is the interplay between ideas used to study the propagation of singularities for the wa...

This book presents the classical theorems about simply connected smooth 4-manifolds: intersection forms and homotopy type, oriented and spin bordism, the index theorem, Wall's diffeomorphisms and h-cobordism, and Rohlin's theorem. Most of the proofs are n...

The notion of a Frobenius structure on a complex analytic manifold appeared at the end of the seventies in the theory of singularities of holomorphic functions. Motivated by physical considerations, further development of the theory has opened new perspec...

A topological embedding is a homeomorphism of one space onto a subspace of another. The book analyzes how and when objects like polyhedra or manifolds embed in a given higher-dimensional manifold. The main problem is to determine when two topological embe...

The past two decades have brought explosive growth in 4-manifold theory. Many books are currently appearing that approach the topic from viewpoints such as gauge theory or algebraic geometry. This volume, however, offers an exposition from a topological p...

Dr. Mills has built on the field generally known as Quantum Mechanics by deriving a new atomic theory of Classical Quantum Mechanics (CQM) from first principles, which unifies Maxwell's Equations, Newton's Laws, and Einstein's General and Special Relativi...

Part I of this volume surveys the developments in the analysis of nonlinear phenomena in Japan during the past decade, while Part II consists of up-to-date original papers concerning qualitative theories and their applications. Dealt with here are nonline...

I was involved in the design of the ARPAnet Protocols and worked on Internet protocols. For about a year I was the chair of of the ISO Presentation Layer committee. I have a lot of first-hand experience with where we are today and how we got here. I've...

This book is an introduction to pattern theory, the theory behind the task of analyzing types of signals that the real world presents to us. It deals with generating mathematical models of the patterns in those signals and algorithms for analyzing the dat...

This collection of English and Spanish articles brings together the latest scholarship on Mexican unrest by researchers in both the United States and Mexico. The contributors use the economic, social and cultural situations in Mexico throughout its histor...

This book constitutes the refereed proceedings of the 34th Symposium of the German Association for Pattern Recognition, DAGM 2012, and the 36th Symposium of the Austrian Association for Pattern Recognition, OAGM 2012, held in Graz, Austria, in August 2012...