Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-23T02:41:52.078Z Has data issue: false hasContentIssue false
  • English
  • Français

SYSTOLIC FILLINGS OF SURFACES

Part of: Graph theory Low-dimensional topology

Published online by Cambridge University Press:  28 August 2018

BIDYUT SANKI Open the ORCID record for BIDYUT SANKI [Opens in a new window]
BIDYUT SANKI*
Affiliation:
Institute of Mathematical Sciences, CIT Campus, Tharamani, Chennai, 600113, India email [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A filling of a closed hyperbolic surface is a set of simple closed geodesics whose complement is a disjoint union of hyperbolic polygons. The systolic length is the length of a shortest essential closed geodesic on the surface. A geodesic is called systolic, if the systolic length is realised by its length. For every $g\geq 2$, we construct closed hyperbolic surfaces of genus $g$ whose systolic geodesics fill the surfaces with complements consisting of only two components. Finally, we remark that one can deform the surfaces obtained to increase the systole.

Keywords

hyperbolic surfacesystolefillingfat graph

MSC classification

Primary: 57M15: Relations with graph theory
Secondary: 05C10: Planar graphs; geometric and topological aspects of graph theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 98 , Issue 3 , December 2018 , pp. 502 - 511
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

References

Anderson, J. W., Parlier, H. and Pettet, A., ‘Relative shapes of thick subsets of moduli space’, Amer. J. Math. 138(2) (2016), 473–498.Google Scholar
Anderson, J. W., Parlier, H. and Pettet, A., ‘Small filling sets of curves on a surface’, Topology Appl. 158 (2011), 84–92.Google Scholar
Aougab, T. and Huang, S., ‘Minimally intersecting filling pairs on surfaces’, Algebraic Geom. Topol. 15 (2015), 903–932.Google Scholar
Fanoni, F. and Parlier, H., ‘Filling sets of curves on punctured surfaces’, New York J. Math. 22 (2016), 653–666.Google Scholar
Thurston, W., ‘A spine for Teichmüller space’, Preprint, 1986.Google Scholar
Beardon, A. F., The Geometry of Discrete Groups (Springer, Berlin–Heidelberg, 1983).Google Scholar
Sanki, B., ‘Filling of closed surfaces’, J. Topol. Anal. (2017), to appear, doi:10.1142/S1793525318500309.Google Scholar