Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · math/0612128

Lengths of geodesics on non-orientable hyperbolic surfaces

Paul Norbury
View original source ↗Read source document ↗Export metadata ↓

Abstract

We give an identity involving sums of functions of lengths of simple closed geodesics, known as a McShane identity, on any non-orientable hyperbolic surface with boundary which generalises Mirzakhani's identities on orientable hyperbolic surfaces with boundary.

Explore related subjects

math.GTmath.DG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Paul Norbury. 2007-06-12. Lengths of geodesics on non-orientable hyperbolic surfaces. https://arxiv.org/abs/math/0612128

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

The Burau representation of the braid group is faithful for n = 4

In this paper we use ideas introduced earlier by Moody, Long, Long-Paton, and Bigelow to prove the theorem of the title, that the Burau representation of the classical braid group is faithful for n = 4. An immediate corollary is that the Jones representation of the braid group is also faithful for n = 4.

math.GT↗
arXiv2026

The Lorenz braid index and hyperbolic volume

A result of Futer, Kalfagianni, and Purcell implies that an upper volume bound for all link complements in the 3-sphere cannot depend solely on the braid index. In this paper, we introduce the Lorenz braid index and generalise the bunch algorithm to provide a general upper volume bound for all link complements in the 3-sphere. Such an upper bound is a quadratic polynomial in the Lorenz braid index. In addition, we construct an explicit family of hyperbolic Lorenz knots for which the classical braid index and the Seifert genus both tend to infinity, while the Lorenz braid index remains bounded.

math.GT↗