Page History

h1. {color:#000000}Subcritical manifolds and algebraic structures{color}

In the morning we will go through the computation of symplectic cohomology for affine space. Using Cieliebak's result that subcritical Weinstein manifolds split, we'll obtain a computation for this class of manifolds.

# Compute the symplectic cohomology of the ball following the outline in Section (3f) of \[Seidel\]. The easiest way to do this is to follow the second approach, and compute the Conley-Zehnder index of the unique time-1 Hamiltonian orbit of the function
{latex}$\tau |z|^2${latex} when  {latex}
$\tau${latex} is not a multiple of {latex}
$ \pi${latex}.
# Introduce the notion of a Weinstein manifold, and that of a subcritical Weinstein manifold. Explain Cieliebak's splitting result for subcritical manifolds (see Theorem 14.16 of \[Cieliebak-Eliashberg\]).
# Explain the statement of the main result of \[Oancea-K\]. Use this to compute symplectic cohomology for subcritical Weinstein manifolds.

In the afternoon, we will discuss algebraic structures on symplectic cohomology.

# Discuss the construction of operations on symplectic cohomology coming from moduli spaces of Riemann surface. Make sure to include a discussion of the BV operator. The construction of these operations is outlined in Section (8a) of \[Seidel\], which \[Ritter\] elaborates upon.
# Define the product on symplectic cohomology by counting pairs of pants. Explain the proof of associativity, and the construction of the unit.
# (Jo Nelson) Use the higher analogues, to define {latex}
$S^1${latex} equivariant symplectic cohomology. Introduce contact homology, and outline the construction of an isomorphism between {latex}
$S^1${latex} equivariant symplectic cohomology and contact homology.