T. Januszkiewicz
4-dimensional locally CAT(0)-manifolds with no Riemannian smoothings.
Wed, 02/24/2010 - 16:01 — SomNambulAuthors: T. Januszkiewicz, J.-F. Lafont, M. Davis
Subjects: Metric Geometry
AbstractWe construct examples of smooth 4-dimensional manifolds M supporting a
locally CAT(0)-metric, whose universal cover X satisfy Hruska's isolated flats
condition, and contain 2-dimensional flats F with the property that the
boundary at infinity of F defines a nontrivial knot in the boundary at infinity
of X. As a consequence, we obtain that the fundamental group of M cannot be
isomorphic to the fundamental group of any Riemannian manifold of nonpositive
sectional curvature.Groups possessing extensive hierarchical decompositions.
Wed, 08/26/2009 - 14:58 — SomNambulAuthors: T. Januszkiewicz, P. H. Kropholler, I. J. Leary
Subjects: Group Theory
AbstractKropholler's class of groups is the smallest class of groups which contains
all finite groups and is closed under the following operator: whenever $G$
admits a finite-dimensional contractible $G$-CW-complex in which all stabilizer
groups are in the class, then $G$ is itself in the class. Kropholler's class
admits a hierarchical structure, i.e., a natural filtration indexed by the
ordinals. For example, stage 0 of the hierarchy is the class of all finite
groups, and stage 1 contains all groups of finite virtual cohomological
dimension.
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