A biased view of symplectic cohomology

Abstract

These are lecture notes from my talks at the "Current Developments in Mathematics" conference (Harvard, 2006). They cover a variety of topics involving symplectic cohomology. In particular, a discussion of (algorithmic) classification issues in symplectic and contact topology is included.

37 pages, 2 figures; v2 has added references, slightly expanded discussion of algorithmic recognizability, more balanced account of early developments; v3 has clarifications in the discussion of equivariant symplectic cohomology; v4 with terminology change (Liouville instead of Weinstein), by popular request; v5, one nasty typo removed

References in corpus (5)

• Géométrie de contact: de la dimension trois vers les dimensions supérieures
• Functors and Computations in Floer homology with Applications Part II
• An exact sequence for contact- and symplectic homology
• Fukaya categories and deformations
• Formalism for Relative Gromov-Witten Invariants

Cited by in corpus (10)

• The monotone wrapped Fukaya category and the open-closed string map
• Kuranishi homology and Kuranishi cohomology
• On the combinatorics of exact Lagrangian surfaces
• Exotic symplectic manifolds from Lefschetz fibrations
• Symplectic Divisorial Capping in Dimension 4
• On the embedding complexity of Liouville manifolds
• Combinatorial Reeb dynamics on punctured contact 3-manifolds
• On the complement of a positive normal crossing divisor with no triple intersection in a projective variety
• Unwrapped continuation invariance in Lagrangian Floer theory: energy and $C^0$ estimates
• Fukaya's conjecture on $S^1$-equivariant de Rham complex