By F. Thomas Farrell and L. Edwin Jones
Aspherical manifolds--those whose common covers are contractible--arise classically in lots of components of arithmetic. They ensue in Lie crew concept as yes double coset areas and in man made geometry because the house varieties keeping the geometry. This quantity includes lectures introduced via the 1st writer at an NSF-CBMS local convention on K-Theory and Dynamics, held in Gainesville, Florida in January, 1989. The lectures have been basically concerned about the matter of topologically characterizing classical aspherical manifolds. This challenge has for the main half been solved, however the three- and four-dimensional situations stay an important open questions; Poincare's conjecture is heavily regarding 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 workforce is isomorphic to a discrete, cocompact subgroup of the Lie staff $O(n,1;{\mathbb R})$. one of many book's subject matters is how the dynamics of the geodesic circulation should be mixed with topological keep an eye on thought to check competently discontinuous team activities on $R^n$. the various extra technical themes of the lectures were deleted, and a few extra effects received because the convention are mentioned in an epilogue. The booklet calls for a few familiarity with the fabric contained in a uncomplicated, graduate-level path in algebraic and differential topology, in addition to a few basic differential geometry.
