Abstract:

Contact structures on S^5 exhibit a unique behavior when compared to contact structures on other spheres. In this talk, after reviewing the general picture on spheres and the history, we present a proof that connected sums of Brieskorn contact structures on S^5, in general, are not of Brieskorn type again. The main tool is the mean Euler characteristic of symplectic homology, a general formula by van Koert—Kwon and explicit computations.