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Non-symplectic smooth circle actions on symplectic manifolds

In: Mathematica Slovaca, vol. 62, no. 3
Bogusław Hajduk - Krzysztof Pawałowski - Aleksy Tralle
Detaily:
Rok, strany: 2012, 539 - 550
Kľúčové slová:
symplectic manifold, non-symplectic smooth circle action
O článku:
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.
Ako citovať:
ISO 690:
Hajduk, B., Pawałowski, K., Tralle, A. 2012. Non-symplectic smooth circle actions on symplectic manifolds. In Mathematica Slovaca, vol. 62, no.3, pp. 539-550. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0029-6

APA:
Hajduk, B., Pawałowski, K., Tralle, A. (2012). Non-symplectic smooth circle actions on symplectic manifolds. Mathematica Slovaca, 62(3), 539-550. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0029-6
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