8,641 research outputs found
Involutions of negatively curved groups with wild boundary behavior
We consider pairs (X,Y) where X is a compact, locally CAT(-1) space, and Y is
a totally geodesic subspace. The inclusion induces an embedding of the
boundaries at infinity of the universal covers; we focus on the case where
these are spheres whose dimensions differ by 2. We show that if the embedding
is tame, then it is unknotted. We give examples of pairs for which the
embedding is knotted (and can be realized as the fixed point set of an
involution). We also provide a criterion for knottedness of tame codimension
two spheres in high dimensional (>5) spheres. Corresponding results for
delta-hyperbolic groups are also discussed. Some corollaries give new results
even in the Riemannian manifold case.Comment: 19 page
EZ-structures and topological applications
We introduce the notion of an EZ-structure on a group. Delta-hyperbolic
groups and CAT(0)-groups have EZ-structures. We show torsion-free groups having
an EZ-structure automatically have an action by homeomorphisms on a closed
(high-dimensional) ball, which is well-behaved away from a "bad limit set" in
the boundary of the ball. We show that groups having such an action satisfy the
Novikov conjecture. For torsion-free delta-hyperbolic groups , we also give
a lower bound for the homotopy groups , where is the stable
topological pseudo-isotopy functor.Comment: 21 pages, final version will appear in Comment. Math. Hel
Finite automorphisms of negatively curved Poincare Duality groups
In this paper, we show that if G is a finite p-group (p prime) acting by
automorphisms on a -hyperbolic Poincare Duality group, then the fixed
subgroup is a Poincare Duality group over Z/p. We also provide examples to show
that the fixed subgroup might not even be a Duality group over Z.Comment: 11 pages, 1 figure; revised version has shorter proof for Prop 2.1;
appeared in Geom. Funct. Anal. 14 (2004), pgs. 283-29
On the topology of the space of negatively curved metrics
We show that the space of negatively curved metrics of a closed negatively
curved Riemannian -manifold, , is highly non-connected
Branched covers of hyperbolic manifolds and harmonic maps
We give examples of harmonic maps between negatively curved manifolds with
special properties. These negatively curved manifolds do not have the homotopy
type of a locally symmetric space
Exotic structures and the limitations of certain analytic methods in geometry
In this survey we review some results concerning negatively curved exotic
strucutres (DIFF and PL) and its (unexpected) implications on the limitations
of some analytic methods in geometry. This article is dedicated to the memory
of Armand Borel
Teichm\"uller Spaces and Bundles with Negatively Curved Fibers
We study the Teichm\"uller space of negatively curved metrics on a high
dimensional manifold, with applications to bundles with negatively curved
fibers
A caveat on the convergence of the Ricci flow for pinched negatively curved manifolds
We give examples of pinched negatively curved manifolds for which the Ricci
flow does not converge smoothly
The Teichm\"{u}ller Space of Pinched Negatively Curved Metrics on a Hyperbolic Manifold is not Contractible
For a smooth manifold we define the Teichm\"uller space \cT(M) of all
Riemannian metrics on and the Teichm\"uller space \cT^\epsilon(M) of
-pinched negatively curved metrics on , where
. We prove that if is hyperbolic the natural
inclusion \cT^\epsilon(M)\hookrightarrow\cT(M) is, in general, not
homotopically trivial. In particular, \cT^\epsilon(M) is, in general, not
contractible
The space of nonpositively curved metrics of a negatively curved manifold
We show that the space of nonpositively curved metrics of a negatively curved
manifold is highly non connected
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