Geodesic
Fundamental group of $\operatorname{Symp}(M,\omega )$ with no circle action
Archivum mathematicum, Tome 45 (2009) no. 1, pp. 75-78 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We show that $\pi _1(\operatorname{Symp}(M, \omega ))$ can be nontrivial for $M$ that does not admit any symplectic circle action.
We show that $\pi _1(\operatorname{Symp}(M, \omega ))$ can be nontrivial for $M$ that does not admit any symplectic circle action.
Classification : 53C15, 53D35, 57S05
Keywords: symplectomorphism; circle action 
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Kędra, Jarek. Fundamental group of $\operatorname{Symp}(M,\omega )$ with no circle action. Archivum mathematicum, Tome 45 (2009) no. 1, pp. 75-78. http://geodesic.mathdoc.fr/item/ARM_2009_45_1_a6/

[1] Ahara, K., Hattori, A.: $4$-dimensional symplectic $S^1$-manifolds admitting moment map. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 38 (2) (1991), 251–298. | MR

[2] Anjos, S.: Homotopy type of symplectomorphism groups of $S^2\times S^2$. Geom. Topol. 6 (2002), 195–218, (electronic). | DOI | MR | Zbl

[3] Audin, M.: Torus actions on symplectic manifolds. Progress in Mathematics, vol. 93, Birkhäuser Verlag, Basel, revised edition, 2004. | MR | Zbl

[4] Baldridge, S.: Seiberg-Witten vanishing theorem for $S^1$-manifolds with fixed points. Pacific J. Math. 217 (1) (2004), 1–10. | DOI | MR | Zbl

[5] Karshon, Y.: Periodic Hamiltonian flows on four-dimensional manifolds. Mem. Amer. Math. Soc. 141 (672) (1999), viii+71. | MR | Zbl

[6] Kędra, J.: Evaluation fibrations and topology of symplectomorphisms. Proc. Amer. Math. Soc. 133 (1) (2005), 305–312, (electronic). | DOI | MR | Zbl

[7] Lalonde, F., Pinsonnault, M.: The topology of the space of symplectic balls in rational 4-manifolds. Duke Math. J. 122 (2) (2004), 347–397. | DOI | MR | Zbl

[8] McDuff, D.: Symplectomorphism Groups and almost Complex Structures. In: Essays on geometry and related topics, Vol. 1, 2, 2001, volume 38 of Monogr. Enseign. Math., pp. 527–556. | MR | Zbl

[9] McDuff, D.: The symplectomorphism group of a blow up. Geom. Dedicata 132 (2008), 1–29. | DOI | MR | Zbl

[10] McDuff, D., Salamon, D.: Introduction to symplectic topology. Oxford Math. Monogr. (1998), Second edition. | MR