Mathematical Research Letters

Volume 20 (2013)

Number 5

Proof of the index conjecture in Hofer geometry

Pages: 981 – 984



Yasha Savelyev (Centre de Recherches Mathématiques, Université de Montréal, Québec, Canada)


Let $\gamma$ be an Ustilovsky geodesic and $H$ its generating function. We give a simple proof of a generalization of the conjecture stated in [7], relating the Morse index of $\gamma$, as a critical point of the Hofer length functional, with the Conley Zehnder index of the extremizers of $H$, considered as periodic orbits.

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