Small filling sets of curves on a surface
- Anderson, James W. School of Mathematics, University of Southampton, UK
- Parlier, Hugo Department of Mathematics, University of Fribourg, Switzerland
- Pettet, Alexandra Department of Mathematics, University of Michigan, Ann Arbor, USA - Mathematical Institute, University of Oxford, UK
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27.10.2010
Published in:
- Topology and its Applications. - 2011, vol. 158, no. 1, p. 84-92
English
We show that the asymptotic growth rate for the minimal cardinality of a set of simple closed curves on a closed surface of genus g which fill and pairwise intersect at most Kgreater-or-equal, slanted1 times is View the MathML source as g→∞. We then bound from below the cardinality of a filling set of systoles by g/log(g). This illustrates that the topological condition that a set of curves pairwise intersect at most once is quite far from the geometric condition that such a set of curves can arise as systoles.
- Faculty
- Faculté des sciences et de médecine
- Department
- Département de Mathématiques
- Language
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- English
- Classification
- Mathematics
- License
- License undefined
- Identifiers
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- RERO DOC 21809
- DOI 10.1016/j.topol.2010.10.007
- Persistent URL
- https://folia.unifr.ch/unifr/documents/301702
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