Alexandra Pettet
Periodic maximal flats are not peripheral.
Thu, 09/17/2009 - 10:33 — SomNambulAuthors: Alexandra Pettet, Juan Souto
Subjects: Geometric Topology
AbstractWe prove that every non-positively curved locally symmetric manifold M of
finite volume contains a compact set K such that no periodic maximal flat can
be homotoped out of K.Small filling sets of curves on a surface.
Fri, 09/11/2009 - 19:12 — SomNambulAuthors: James W. Anderson, Hugo Parlier, Alexandra Pettet
Subjects: Geometric Topology
AbstractConsider a set of simple closed curves on a surface of genus $g$ which fill
the surface and which pairwise intersect at most once. We show that the
asymptotic growth rate of the smallest number in such a set is $2\sqrt{g}$ as
$g \to \infty$. More generally, we give a precise asymptotic for filling sets
of curves which pairwise intersect at most $K \geq 1$ times. We then bound from
below the cardinality of a filling set of {\it systoles} by
$\frac{g}{\log(g)}$.Small filling sets of curves on a surface.
Fri, 09/11/2009 - 19:12 — SomNambulAuthors: James W. Anderson, Hugo Parlier, Alexandra Pettet
Subjects: Geometric Topology
AbstractConsider a set of simple closed curves on a surface of genus $g$ which fill
the surface and which pairwise intersect at most once. We show that the
asymptotic growth rate of the smallest number in such a set is $2\sqrt{g}$ as
$g \to \infty$. More generally, we give a precise asymptotic for filling sets
of curves which pairwise intersect at most $K \geq 1$ times. We then bound from
below the cardinality of a filling set of {\it systoles} by
$\frac{g}{\log(g)}$.
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