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arXiv · 1207.2228

Descent and C^0-rigidity of spectral invariants on monotone symplectic manifolds

Sobhan Seyfaddini
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Abstract

We obtain estimates showing that on monotone symplectic manifolds (asymptotic) spectral invariants of Hamiltonians which vanish on a non-empty open set, U, descend to Ham_c(M\setminus U) from its universal cover. Furthermore, we show these invariants and are continuous with respect to the C^0-topology on Ham_c(M\setminus U). We apply these results to Hofer geometry and establish unboundedness of the Hofer diameter of $Ham_c(M\setminus U)$ for stably displaceable $U$. We also answer a question of F. Le Roux about $C^0$-continuity properties of the Hofer metric.

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Sobhan Seyfaddini. 2012-07-11. Descent and C^0-rigidity of spectral invariants on monotone symplectic manifolds. https://doi.org/10.1142/s1793525312500215

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