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
Published in:
 Topology and its Applications.  2011, vol. 158, no. 1, p. 8492
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 Kgreaterorequal, 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

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Mathematics

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https://folia.unifr.ch/unifr/documents/301702
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