Subcritical manifolds and algebraic structures">Subcritical manifolds and algebraic structures

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.

1. 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
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   $\tau |z|^2$

    when  
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   $\tau$

    is not a multiple of 
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   $ \pi$

   .
2. 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]).
3. 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.

1. The product on symplectic cohomology is defined by counting pairs of pants. Explain the proof of associativity, and the construction of the unit. The construction of these operations is outlined in Section (8a) of [Seidel], which [Ritter] elaborates upon.
2. Define the BV operator, and use it, and its higher analogues, to define
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   $S^1$

    equivariant symplectic cohomology.
3. Introduce contact homology, and outline the construction of an isomorphism between 
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   $S^1$

    equivariant symplectic cohomology and contact homology.