Curve shortening and the topology of closed geodesics on surfaces

Details Curve shortening and the topology of closed geodesics on surfaces Curve shortening and the topology of closed geodesics on surfaces

2007-05-21

arxiv.org/abs/0705.3012v1

Ann. of Math. (2) 162 (2005), no. 3, 1187--1241

Mathematics

Differential Geometry

55 pages, published version

Scientific paper

We study "flat knot types" of geodesics on compact surfaces M^2. For every
flat knot type and any Riemannian metric g we introduce a Conley index
associated with the curve shortening flow on the space of immersed curves on
M^2. We conclude existence of closed geodesics with prescribed flat knot types,
provided the associated Conley index is nontrivial.

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