Projections in the curve complex arising from covering maps

Robert Tang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Let P: ∑ → S be a finite degree covering map between surfaces. Rafi and Schleimer showed that there is an induced quasi-isometric embedding Π: C(S) → C(∑) between the associated curve complexes. We define an operation on curves in C(∑) using minimal intersection number conditions and prove that it approximates a nearest point projection to Π(C(S)). We also approximate hulls of finite sets of vertices in the curve complex, together with their corresponding nearest point projections, using intersection numbers.

Original languageEnglish
Pages (from-to)213-239
Number of pages27
JournalPacific Journal of Mathematics
Issue number1
Publication statusPublished - 2017
Externally publishedYes


  • Covering map
  • Curve complex
  • Hull
  • Nearest point projection

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