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SUMMARY:Sílvia Anjos (Instituto Superior Técnico and CAMGSD)
DTSTART:20201117T170000Z
DTEND:20201117T180000Z
DTSTAMP:20260423T022619Z
UID:Geolis/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Geolis/16/">
 Loops in the fundamental group of $\\mathrm{Symp}(M\,\\omega)$ which are n
 ot represented by circle actions</a>\nby Sílvia Anjos (Instituto Superior
  Técnico and CAMGSD) as part of Geometria em Lisboa (IST)\n\n\nAbstract\n
 It was observed by J. Kędra that there are many symplectic 4-manifolds $(
 M\, \\omega)$\, where $M$ is neither rational nor ruled\, that admit no ci
 rcle action and $\\pi_1 (\\mathrm{Ham}( M))$ is nontrivial. In the case $M
 ={\\mathbb C\\mathbb P}^2\\#\\\,k\\overline{\\mathbb C\\mathbb P}\\\,\\!^2
 $\, with $k \\leq 4$\, it follows from the work of several authors that th
 e full rational homotopy of $\\mathrm{Symp}(M\,\\omega)$\, and in particul
 ar their fundamental group\, is generated by circle actions on the manifol
 d. In this talk we study loops in the fundamental group of $\\mathrm{Symp}
 _h({\\mathbb C\\mathbb P}^2\\#\\\,5\\overline{\\mathbb C\\mathbb P}\\\,\\!
 ^2) $ of symplectomorphisms that act trivially on homology\, and show that
 \, for some particular symplectic forms\, there are loops which cannot be 
 realized by circle actions. Our work depends on Delzant classification of 
 toric symplectic manifolds and Karshon's classification of Hamiltonian cir
 cle actions\n\nThis talk is based in joint work with Miguel Barata\, Marti
 n Pinsonnault and Ana Alexandra Reis.\n
LOCATION:https://researchseminars.org/talk/Geolis/16/
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