Geometry & Topology Monographs 2 (1999), Proceedings of the Kirbyfest, paper no. 11, pages 201-213.

Configurations of curves and geodesics on surfaces

Joel Hass, Peter Scott

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.

Keywords. Geodesics, configurations, curves on surfaces, double points

AMS subject classification. Primary: 53C22. Secondary: 57R42.

E-print: arXiv:math.GT/9903130

Submitted: 22 March 1999. (Revised: 23 August 1999.) Published: 18 November 1999.

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Joel Hass, Peter Scott

Department of Mathematics, University of California
Davis, CA 95616, USA

Department of Mathematics, University of Michigan
Ann Arbor, MI 48109, USA

Email: hass@math.ucdavis.edu, pscott@math.lsa.umich.edu

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