Abstract
On any surface we give an example of a metric that contains simple closed geodesics with arbitrarily high Morse index. Similarly, on any $3$-manifold we give an example of a metric that contains embedded minimal tori with arbitrarily 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.ADDHERE
Citation
Tobias H. Colding. Nancy Hingston. "Metrics without Morse index bounds." Duke Math. J. 119 (2) 345 - 365, 15 August 2003. https://doi.org/10.1215/S0012-7094-03-11925-0
Information
