Brieskorn Manifolds, Positive Sasakian Geometry, and Contact Topology

  title={Brieskorn Manifolds, Positive Sasakian Geometry, and Contact Topology},
  author={Charles P. Boyer and Leonardo Macarini and Otto van Koert},
  journal={arXiv: Differential Geometry},
Using $S^1$-equivariant symplectic homology, in particular its mean Euler characteristic, of the natural filling of links of Brieskorn-Pham polynomials, we prove the existence of infinitely many inequivalent contact structures on various manifolds, including in dimension 5 the k-fold connected sums of $S^2\times S^3$ and certain rational homology spheres. We then apply our result to show that on these manifolds the moduli space of classes of positive Sasakian structures has infinitely many… 
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