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

Magee, Michael

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