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 crew idea as sure double coset areas and in man made geometry because the area types conserving the geometry. This quantity includes 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 basically focused on 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 crucial open questions; Poincare's conjecture is heavily relating to the three-d 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 primary staff is isomorphic to a discrete, cocompact subgroup of the Lie crew $O(n,1;{\mathbb R})$. one of many book's issues is how the dynamics of the geodesic circulation will be mixed with topological regulate conception to check effectively discontinuous workforce activities on $R^n$. a few of the extra technical issues of the lectures were deleted, and a few extra effects bought because the convention are mentioned in an epilogue. The booklet 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 simple differential geometry.

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