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Geometry, Topology, and Dynamics in Negative Curvature
Ten high-quality survey articles provide an overview of important recent developments in the mathematics surrounding negative curvature.
Classical Aspherical Manifolds
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.
High-Dimensional Manifold Topology
Contents: A Foliated Squeezing Theorem for Geometric Modules (A Bartels et al.)Equivariant Cellular Homology and Its Applications (B Chorny)Remarks on a Conjecture of Gromov and Lawson (W Dwyer et al.)Chain Complex Invariants for Group Actions (L E Jones)The Ore Condition, Affiliated Operators, and the Lamplighter Group (P A Linnell et al.)The Surgery Exact Sequence Revisited (E K Pedersen)K-theory for Proper Smooth Actions of Totally Disconnected Groups (J Sauer)Geometric Chain Homotopy Equivalences between Novikov Complexes (D Schütz)and other papers Readership: Graduate students and researchers in geometry and topology. Keywords:High-Dimensional Manifold Topology;Operator Algebras;K-Theory;L-Theory;Foliated Control Theory
Classical Aspherical Manifolds
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.
Markov Cell Structures near a Hyperbolic Set
The authors' argument is a spiritual descendent of earlier work of Adler and Weiss, Sinaĭ, and Bowen, and involves a close study of triangulations. The discussion is long and technical, but the outline of the proof is sketched clearly in Section 1 for the special case of [italic]F an expanding immersion. A concluding section lists problems on hyperbolic sets, Markov partitions, and related matters; remarks on topological invariants, including the conjectured vanishing of Pontryagin classes for manifolds supporting Anosov diffeomorphisms, may be of particular interest.
U.S. Army Register
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