Symplectic homology of some Brieskorn manifolds

Vendredi 10 avril 2015 15:30-16:30 - Peter Uebele - Augsburg

Résumé : Brieskorn manifolds became prominent in contact topology after I.\ Ustilovsky used them to prove the existence of infinitely many contact structures on $S^4m+1$. After briefly reviewing his result, I will focus on another class of Brieskorn manifolds for which contact homology cannot distinguish the contact structures, whereas (positive) symplectic homology can. The main difficulty of the proof lies in the computation of the differential of symplectic homology. For this, we will use Morse—Bott methods as well as an explicit perturbation, combined with a symmetry of the underlying manifold. If time permits, I will also comment on how the resulting transversality problem can be resolved.

Lieu : 425 à Orsay - 117-119

Symplectic homology of some Brieskorn manifolds  Version PDF