Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 
 
 

 

Hyperbolic surfaces with long systoles that form a pants decomposition


Author: Bram Petri
Journal: Proc. Amer. Math. Soc. 146 (2018), 1069-1081
MSC (2010): Primary 30F10; Secondary 53C22, 57M50
DOI: https://doi.org/10.1090/proc/13806
Published electronically: September 13, 2017
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We present a construction of sequences of closed hyperbolic surfaces that have long systoles which form pants decompositions of these surfaces. The length of the systoles of these surfaces grows logarithmically as a function of their genus.


References [Enhancements On Off] (What's this?)

  • [BS94] P. Buser and P. Sarnak, On the period matrix of a Riemann surface of large genus, Invent. Math. 117 (1994), no. 1, 27-56. With an appendix by J. H. Conway and N. J. A. Sloane. MR 1269424, https://doi.org/10.1007/BF01232233
  • [Bus78] Peter Buser, Riemannsche Flächen mit grosser Kragenweite, Comment. Math. Helv. 53 (1978), no. 3, 395-407 (German). MR 505554, https://doi.org/10.1007/BF02566086
  • [Bus10] Peter Buser, Geometry and spectra of compact Riemann surfaces, Modern Birkhäuser Classics, Birkhäuser Boston, Inc., Boston, MA, 2010. Reprint of the 1992 edition. MR 2742784
  • [ES63] Paul Erdős and Horst Sachs, Reguläre Graphen gegebener Taillenweite mit minimaler Knotenzahl, Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg Math.-Natur. Reihe 12 (1963), 251-257 (German). MR 0165515
  • [FP15] Federica Fanoni and Hugo Parlier, Systoles and kissing numbers of finite area hyperbolic surfaces, Algebr. Geom. Topol. 15 (2015), no. 6, 3409-3433. MR 3450766, https://doi.org/10.2140/agt.2015.15.3409
  • [KSV07] Mikhail G. Katz, Mary Schaps, and Uzi Vishne, Logarithmic growth of systole of arithmetic Riemann surfaces along congruence subgroups, J. Differential Geom. 76 (2007), no. 3, 399-422. MR 2331526
  • [Par06] Hugo Parlier, Hyperbolic polygons and simple closed geodesics, Enseign. Math. (2) 52 (2006), no. 3-4, 295-317. MR 2300612
  • [Par14] Hugo Parlier, Simple closed geodesics and the study of Teichmüller spaces, Handbook of Teichmüller theory. Vol. IV, IRMA Lect. Math. Theor. Phys., vol. 19, Eur. Math. Soc., Zürich, 2014, pp. 113-134. MR 3289700, https://doi.org/10.4171/117-1/3
  • [PW15] Bram Petri and Alexander Walker, Graphs of large girth and surfaces of large systole, ArXiv 1512.06839 (2015).
  • [Sch94] Paul Schmutz, Congruence subgroups and maximal Riemann surfaces, J. Geom. Anal. 4 (1994), no. 2, 207-218. MR 1277506, https://doi.org/10.1007/BF02921547
  • [SS98] Paul Schmutz Schaller, Geometry of Riemann surfaces based on closed geodesics, Bull. Amer. Math. Soc. (N.S.) 35 (1998), no. 3, 193-214. MR 1609636, https://doi.org/10.1090/S0273-0979-98-00750-2

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 30F10, 53C22, 57M50

Retrieve articles in all journals with MSC (2010): 30F10, 53C22, 57M50


Additional Information

Bram Petri
Affiliation: Max Planck Institute for Mathematics, Bonn, Germany
Address at time of publication: Mathematical Institute, University of Bonn, Bonn, Germany
Email: bpetri@math.uni-bonn.edu

DOI: https://doi.org/10.1090/proc/13806
Received by editor(s): September 22, 2016
Received by editor(s) in revised form: February 28, 2017, and April 6, 2017
Published electronically: September 13, 2017
Communicated by: David Futer
Article copyright: © Copyright 2017 American Mathematical Society

American Mathematical Society