Symplectic homology of some Brieskorn manifolds

Abstract

This paper consists of two parts. In the first part, we use symplectic homology to distinguish the contact structures on the Brieskorn manifolds $\Sigma (2l,2,2,2)$, which contact homology cannot distinguish. This answers a question from [22]. In the second part, we prove the existence of infinitely many exotic but homotopically trivial exotic contact structures on $S^7$, distinguished by the mean Euler characteristic of $S^1$-equivariant symplectic homology. Apart from various connected sum constructions, these contact structures can be taken from the Brieskorn manifolds $\Sigma (78k+1,13,6,3,3)$. We end with some considerations about extending this result to higher dimensions.

33 pages; several small corrections. To appear in Mathematische Zeitschrift. The final publication is available at http://link.springer.com/article/10.1007/s00209-015-1596-3

References in corpus (1)

• Displaceability and the mean Euler characteristic

Cited by in corpus (5)

• Symplectic Homology of complements of smooth divisors
• Vanishing of Symplectic Homology and Obstruction to Flexible Fillability
• Reduced symplectic homology and string topology
• Connected sums of Brieskorn contact $5$-spheres
• Symplectic cohomology of quasihomogeneous $c{A}_n$ singularities