Page History

h1. {color:#000000}Cotangent bundles and Viterbo Functoriality{color}

In the morning, we will go through one method of computing the symplectic cohomology of cotangent bundles. 

# Show that the unit cotangent bundle is a Liouville domain. Explain the correspondence between closed geodesics and Reeb orbits. State the isomorphism between symplectic cohomology and the homology of the free loop space (Theorem 3.5 in \[Seidel\]). Give the statement only with
{latex}$\mathbb{Z} / 2\mathbb{Z}${latex} coefficients.
# Define the Morse homology of the free loop space following Section 2 of \[Abbondandolo-Schwarz\].
# Explain the Abbondandolo-Schwarz construction of an isomorphism between symplectic cohomology and the homology of the free loop space, following Section 3 of \[Abbondandolo-Schwarz\]. Make sure to draw the pictures that are associated to these maps (i.e. counting pseudo-holomorphic half-cylinders in the cotangent bundle followed by gradient flow lines in the base).

In the afternoon,

# Define the notion of a Liouville subdomain. Give examples coming from exact Lagrangian embeddings, and from Weinstein handle attachment.
# Explain the construction of Section 2 in \[Viterbo\] associating maps on symplectic cohomology to Liouville subdomains. Warning: what Viterbo denotes {latex}
$FH^*${latex} is the dual of the theory Seidel denotes {latex}$SH^*$ {latex}. To keep this talk consistent with the others, you should dualise Viterbo's statements.