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Counting one-sided simple closed geodesics on Fuchsian thrice punctured projective planes.

Magee, Michael (2020) 'Counting one-sided simple closed geodesics on Fuchsian thrice punctured projective planes.', International mathematics research notices., 2020 (13). pp. 3886-3901.


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.

Item Type:Article
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Publisher 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:
Date accepted:03 May 2018
Date deposited:10 July 2018
Date of first online publication:14 June 2018
Date first made open access:30 June 2020

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