Skip to main content

Research Repository

Advanced Search

Counting One-Sided Simple Closed Geodesics on Fuchsian Thrice Punctured Projective Planes

Magee, Michael

Counting One-Sided Simple Closed Geodesics on Fuchsian Thrice Punctured Projective Planes Thumbnail


Authors



Abstract

We prove that there is a true asymptotic formula for the number of one-sided simple closed curves of length ≤ L on any Fuchsian real projective plane with three points removed. The exponent of growth is independent of the hyperbolic metric, and it is noninteger, in contrast to counting results of Mirzakhani for simple closed curves on orientable Fuchsian surfaces.

Citation

Magee, M. (2020). Counting One-Sided Simple Closed Geodesics on Fuchsian Thrice Punctured Projective Planes. International Mathematics Research Notices, 2020(13), 3886-3901. https://doi.org/10.1093/imrn/rny112

Journal Article Type Article
Acceptance Date May 3, 2018
Online Publication Date Jun 14, 2018
Publication Date 2020-07
Deposit Date Jul 10, 2018
Publicly Available Date Jun 30, 2020
Journal International Mathematics Research Notices
Print ISSN 1073-7928
Electronic ISSN 1687-0247
Publisher Oxford University Press
Peer Reviewed Peer Reviewed
Volume 2020
Issue 13
Pages 3886-3901
DOI https://doi.org/10.1093/imrn/rny112

Files

Accepted Journal Article (337 Kb)
PDF

Copyright Statement
This is a pre-copyedited, author-produced PDF of an article accepted for publication in International Mathematics Research Notices following peer review. The version of record Magee, Michael (2020). Counting One-Sided Simple Closed Geodesics on Fuchsian Thrice Punctured Projective Planes. International Mathematics Research Notices 2020(13): 3886-3901.
is available online at: https://doi.org/10.1093/imrn/rny112





You might also like



Downloadable Citations