Counting curve types

Abstract:Let $S$ be a closed orientable hyperbolic surface, and let $\cal{O}(K,S)$ denote the number of mapping class group orbits of curves on $S$ with at most $K$ self-intersections. Building on work of Sapir, we give upper and lower bounds for $\cal(K,S)$ which are both exponential in $\sqrt{K}$.

• Publication year

  2016

• Venue

  American Journal of Mathematics

• Publication date

  2016-06-20

• Fields of study

  Mathematics

• Identifiers
  DOI 10.1353/ajm.2018.0043arXiv 1606.06067
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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