Metrics without Morse index bounds

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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.
To appear in Duke Mathematical journal

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Geometric Topology, Differential Geometry

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http://salesiana.dossiersoluciones.com/handle/123456789/65350

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0210290
 http://arxiv.org/abs/math/0210290

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arXiv