The proof of the index conjecture in Hofer geometry

Details The proof of the index conjecture in Hofer geometry The proof of the index conjecture in Hofer geometry

2012-04-13

arxiv.org/abs/1204.3098v1

Mathematics

Symplectic Geometry

4pgs

Scientific paper

Let $\gamma$ be an $S^1$-subgroup in $Ham (M, \omega)$ generated by a Morse
Hamiltonian $H$. We give a simple proof of the conjecture stated in
\cite{virtmorse}, relating the Morse index of $ \gamma$, as a critical point of
the Hofer length functional, with the Conley Zehnder index of the extremizer
$x_{\max}$ of $ H$, considered as a periodic orbit of $H$.

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