Journal article

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. 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.
Faculté des sciences et de médecine
Département de Mathématiques
  • English
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