2002/10/18 by Tobias H. Colding, Colding, Tobias H., Nancy Hingston +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #math.DG #math.GT
paper · pdf · doi:10.48550/arxiv.math/0210290
To appear in Duke Mathematical journal
arxiv created 2002/10/18 · arxiv updated 2009/11/30
On any surface we give an example of a metric that contains simple closed geodesics with arbitrary high Morse index. Similarly, on any 3-manifold we give an example of a metric that contains embedded minimal tori with arbitrary high Morse index. Previously no such examples were known. We also discuss whether or not such bounds should hold for a generic metric and why bumpy does not seem to be the right generic notion. Finally, we mention briefly what such bounds might be used for.