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Configurations of curves and geodesics on surfaces

1999/03/31 by Joel Hass, Peter Scott
Mathematics · #math.GT #math.DG #msc:53C22 #msc:57R42

paper · pdf

published as Geom. Topol. Monogr. 2 (1999), 201-213 · 13 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTMon2/paper11.abs.html

arxiv created 1999/11/18 · arxiv updated 2009/11/30

Abstract

We study configurations of immersed curves in surfaces and surfaces in 3-manifolds. Among other results, we show that primitive curves have only finitely many configurations which minimize the number of double points. We give examples of minimal configurations not realized by geodesics in any hyperbolic metric.

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