Bounded symplectic diffeomorphisms and split flux groups

Diffeomorphisms, Symplectic Forms, and Kodaira Fibrations

As was recently pointed out by McMullen and Taubes [6], there are 4manifolds for which the diffeomorphism group does not act transitively on the deformation classes of orientation-compatible symplectic structures. This note points out a huge class of rather different examples, arising as orientation-reversed versions of some complex surfaces constructed by Kodaira [3]. Supported in part by NSF ...

Theta functions on covers of symplectic groups

We study the automorphic theta representation $Theta_{2n}^{(r)}$ on the $r$-fold cover of the symplectic group $Sp_{2n}$‎. ‎This representation is obtained from the residues of Eisenstein series on this group‎. ‎If $r$ is odd‎, ‎$nle r

Diffeomorphisms Preserving Symplectic Data on Submanifolds

We characterize general symplectic manifolds and their structure groups through a family of isotropic or symplectic submanifolds and their diffeomorphic invariance. In this way we obtain a complete geometric characterization of symplectic diffeomorphisms and a reinterpretation of symplectomorphisms as diffeomorphisms acting purely on isotropic or symplectic submanifolds. DOI: 10.1134/S008154380...

On Groups of Diffeomorphisms

I. We consider here the groups of homeomorphisms on Euclidean w-space and the «-sphere Sn. Chiefly we will be concerned with the question of whether or not these groups reduce in an homotopy sense to the ordinary orthogonal group acting on these spaces. Such questions are intimately connected with the theory of fibre bundles in which these spaces occur as fibres. We will restrict ourselves to t...

Groups of Circle Diffeomorphisms