Hugo Parlier
Simple closed geodesics and the study of Teichm\"uller spaces.
Wed, 12/09/2009 - 16:01 — SomNambulAuthors: Hugo Parlier
Subjects: Geometric Topology
AbstractThe goal of the chapter is to present certain aspects of the relationship
between the study of simple closed geodesics and Teichm\"uller spaces.Bers' constants for punctured spheres and hyperelliptic surfaces.
Mon, 11/30/2009 - 16:01 — SomNambulAuthors: Hugo Parlier, Florent Balacheff
Subjects: Geometric Topology
AbstractThis article is dedicated to prove Buser's conjecture about Bers' constants
for spheres with cusps (or marked points) and for hyperelliptic surfaces. More
specifically, our main theorem states that any hyperbolic sphere with $n$ cusps
has a pants decomposition with all of its geodesics of length bounded by a
constant roughly square root of $n$. Other results include lower and upper
bounds for Bers' constants for hyperelliptic surfaces and spheres with boundary
geodesics.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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