By F. Thomas Farrell and L. Edwin Jones

Aspherical manifolds--those whose common covers are contractible--arise classically in lots of parts of arithmetic. They happen in Lie workforce concept as definite double coset areas and in man made geometry because the area types protecting the geometry. This quantity comprises lectures introduced by way of the 1st writer at an NSF-CBMS nearby convention on K-Theory and Dynamics, held in Gainesville, Florida in January, 1989. The lectures have been essentially involved in the matter of topologically characterizing classical aspherical manifolds. This challenge has for the main half been solved, however the three- and four-dimensional instances stay an important open questions; Poincare's conjecture is heavily with regards to the three-dimensional challenge. one of many major effects is closed aspherical manifold (of size $\neq$ three or four) is a hyperbolic area if and provided that its basic workforce is isomorphic to a discrete, cocompact subgroup of the Lie crew $O(n,1;{\mathbb R})$. one of many book's topics is how the dynamics of the geodesic circulate might be mixed with topological keep an eye on thought to check safely discontinuous staff activities on $R^n$. the various extra technical issues of the lectures were deleted, and a few extra effects acquired because the convention are mentioned in an epilogue. The publication calls for a few familiarity with the fabric contained in a simple, graduate-level path in algebraic and differential topology, in addition to a few undemanding differential geometry.

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