Non-symplectic smooth circle actions on symplectic manifolds |
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| Authors: | Email author" target="_blank">Bogus?aw?HajdukEmail author Krzysztof?Pawa?owski Aleksy?Tralle |
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| Institution: | 1.Mathematical Institute,Wroc?aw University,Wroc?aw,Poland;2.Department of Mathematics and Information Technology,University of Warmia and Mazury,Olsztyn,Poland;3.Faculty of Mathematics and Computer Science,Adam Mickiewicz University,Poznań,Poland;4.Department of Mathematics and Information Technology,University of Warmia and Mazury,Olsztyn,Poland |
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| Abstract: | We construct smooth circle actions on symplectic manifolds with non-symplectic fixed point sets or cyclic isotropy sets. All
such actions are not compatible with any symplectic form on the manifold in question. In order to cover the case of non-symplectic
fixed point sets, we use two smooth 4-manifolds (one symplectic and one non-symplectic) which become diffeomorphic after taking
the products with the 2-sphere. The second type of actions is obtained by constructing smooth circle actions on spheres with
non-symplectic cyclic isotropy sets, which (by the equivariant connected sum construction) we carry over from the spheres
on products of 2-spheres. Moreover, by using the mapping torus construction, we show that periodic diffeomorphisms (isotopic
to symplectomorphisms) of symplectic manifolds can provide examples of smooth fixed point free circle actions on symplectic
manifolds with non-symplectic cyclic isotropy sets. |
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