352 research outputs found
Tits alternative for closed real analytic 4-manifolds of nonpositive curvature
We study subgroups of fundamental groups of real analytic closed 4-manifolds
with nonpositive sectional curvature. In particular, we are interested in the
following question: if a subgroup of the fundamental group is not virtually
free abelian, does it contain a free group of rank two ? The technique involves
the theory of general metric spaces of nonpositive curvature.Comment: 26 page
A Rigidity Property of Some Negatively Curved Solvable Lie Groups
We show that for some negatively curved solvable Lie groups, all self
quasiisometries are almost isometries. We prove this by showing that all self
quasisymmetric maps of the ideal boundary (of the solvable Lie groups) are
bilipschitz with respect to the visual metric. We also define parabolic visual
metrics on the ideal boundary of Gromov hyperbolic spaces and relate them to
visual metrics
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