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.
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- Novikov Conjectures, Index Theorems, and Rigidity: Volume 1: Oberwolfach 1993 (London Mathematical Society Lecture Note Series) by Steven C. Ferry in Front Matter
- Knots 90: Proceedings of the International Conference on Knot Theory and Related Topics, Held in Osaka (Japan), August 15-19, 19 (Japan, August 15-19, 1990) by Akio Kawauchi on page 44
- The Algebraic Characterization of Geometric 4-Manifolds (London Mathematical Society Lecture Note Series) by J. A. Hillman in Back Matter
- Surveys on Surgery Theory, Vol. 1 by Sylvain Cappell on page 297
- Surveys on Surgery Theory: Volume 2. Papers Dedicated to C.T.C. Wall. (AM-149) (Annals of Mathematics Studies, 149) by Sylvain Cappell on page 37
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