Abstract
The generalization of McShane’s identity for the quotient surface \(\Sigma_q\) of any Hecke group \(H_q\), where q is an integer greater than 3.
Similar content being viewed by others
Change history
05 August 2021
An Erratum to this paper has been published: https://doi.org/10.1007/s13226-021-00160-2
References
A. Beardon, The geometry of discrete groups, Springer-Verlag, New York 1983.
J. Birman, C. Series, An algorithm for simple curves on surfaces, J. London Math. Soc. (2) 29 (1984), 331-342.
K. Farooq, The structural properties of quotient surfaces of a Hecke group, Conform. Geom. Dyn. 23 (2019), 262-282.
G. McShane, A remarkable identity for the length of curves on surfaces, - Ph.D. thesis, University of Warwick, 1991.
G. McShane, Simple geodesics and a series constant over Teichmuller space, Invent. Math. 132 (1998) 607-632.
G. McShane, Weierstrass points and simple geodesics, Bull. London Math. Soc. 36 (2004) 181-187.
G. McShane, Simple geodesics on surfaces of genus two, Annales Academi Scientiarum Fennic 31 (2006) 31-38
A. Haas, The geometry of the hyperelliptic involution in genus two, Proceedings of Amer. Math. Soc. (1) 105 (1989) 159-165.
S.P. Tan, Y.L. Wong & Y. Zhang, Generalisation of McShane’s identity to hyperbolic cone-surfaces, J. Differential Geom. 72 (2006) 73-112.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Gadadhar Misra.
The original online version of this article was revised due to an error in Theorem A.
Rights and permissions
About this article
Cite this article
Farooq, K. A note on the McShane’s identity for Hecke groups. Indian J Pure Appl Math 52, 915–931 (2021). https://doi.org/10.1007/s13226-021-00043-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13226-021-00043-6