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- W1668055286 abstract "By a theorem of Banyaga the group of diffeomorphisms of a manifold $P$ preserving a regular contact form $alpha$ is a central $S^1$ extension of the commutator of the group of symplectomorphisms of the base $B = P/S^1$. We show that if $T$ is a Hamiltonian maximal torus in the group of symplectomorphism of $B$, then its preimage under the extension map is a maximal torus not only in the group $Diff(P, alpha)$ of diffeomorphisms of $P$ preserving $alpha$ but also in the much bigger group of contactomorphisms $Diff (P, xi)$, the group of diffeomorphism of $P$ preserving the contact distribution $xi = ker alpha$. We use this (and the work of Hausmann, and Tolman on polygon spaces) to give examples of contact manifolds $(P, xi = ker alpha)$ with maximal tori of different dimensions in their group of contactomorphisms." @default.
- W1668055286 created "2016-06-24" @default.
- W1668055286 creator A5055475308 @default.
- W1668055286 date "2002-12-03" @default.
- W1668055286 modified "2023-09-27" @default.
- W1668055286 title "On maximal tori in the contactomorphism groups of regular contact manifolds" @default.
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