Abstract
(Non-)displaceability of fibers of integrable systems has been an important problem in symplectic geometry. In this paper, for a large class of classical Liouville integrable systems containing the Lagrangian top, the Kovalevskaya top and the C. Neumann problem, we find a non-displaceable fiber for each of them. Moreover, we show that the non-displaceable fiber which we detect is the unique fiber which is non-displaceable from the zero-section. As a special case of this result, we also show the existence of a singular level set of a convex Hamiltonian, which is non-displaceable from the zero-section. To prove these results, we use the notion of superheaviness introduced by Entov and Polterovich.
Funding Statement
This work has been supported by JSPS KAKENHI Grant Numbers JP18J00765, JP18J00335.
Citation
Morimichi KAWASAKI. Ryuma ORITA. "Rigid fibers of integrable systems on cotangent bundles." J. Math. Soc. Japan 74 (3) 829 - 847, July, 2022. https://doi.org/10.2969/jmsj/84278427
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