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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.

# The productDiscuss the construction of operations on symplectic cohomology iscoming definedfrom bymoduli countingspaces pairsof ofRiemann pantssurface. ExplainMake thesure proofto ofinclude associativity,a anddiscussion the construction of the BV unitoperator. 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 BVproof of operatorassociativity, and use it, and its the construction of the unit.
# (Jo Nelson) Use the higher analogues, to define
 {latex}
# $S^1${latex} equivariant equivariant symplectic cohomology.
# (Jo Nelson) Introduce  Introduce contact homology, and outline the construction of an isomorphism between between {latex}
# $S^1${latex} equivariant equivariant symplectic cohomology and contact homology.