Systoles of Hyperbolic Manifolds

Details Systoles of Hyperbolic Manifolds Systoles of Hyperbolic Manifolds

2010-08-16

arxiv.org/abs/1008.2646v4

Mathematics

Geometric Topology

12 pages; revised following referee's comments; to appear in Algebraic and Geometric Topology

Scientific paper

We show that for every $n\geq 2$ and any $\epsilon>0$ there exists a compact hyperbolic $n$-manifold with a closed geodesic of length less than $\epsilon$. When $\epsilon$ is sufficiently small these manifolds are non-arithmetic, and they are obtained by a generalised inbreeding construction which was first suggested by Agol for $n=4$. We also show that for $n\geq 3$ the volumes of these manifolds grow at least as $1/\epsilon^{n-2}$ when $\epsilon\to 0$.

Affiliated with

Also associated with

No associations

Rating

Systoles of Hyperbolic Manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Systoles of Hyperbolic Manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Systoles of Hyperbolic Manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-177611