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Title: Rigid Fibers of Spinning Tops
Authors: KAWASAKI, Morimichi
ORITA, Ryuma
Author's alias: 川﨑, 盛通
折田, 龍馬
Keywords: 57R17
Symplectic manifolds
groups of Hamiltonian diffeomorphisms
moment maps
symplectic quasi-states
heavy subsets
Issue Date: Aug-2020
Publisher: Research Institute for Mathematical Sciences, Kyoto University
Start page: 1
End page: 17
Thesis number: RIMS-1922
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 zerosection. As a special case of this result, we also show that a singular level set of a convex Hamiltonian is non-displaceable from the zero-section. To prove these results, we use the notion of superheaviness introduced by Entov and Polterovich.
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