Metrics without Morse index bounds
Tobias H. Colding, Nancy Hingston,
2002.10.18
http://arxiv.org/abs/math/0210290
On any surface we give an example of a metric that contains simple closed
geodesics with arbitrary high Morse index. Similarly, on any 3manifold 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.
