The Künneth formula in Floer homology for manifolds with restricted contact type boundary

By A. Oancea. 2004

66 citations recorded by the source corpus.

We prove the Künneth formula in Floer (co)homology for manifolds with restricted contact type boundary. We use Viterbo's definition of Floer homology, involving the symplectic completion by adding a positive cone over the boundary. The Künneth formula implies the vanishing of Floer (co)homology for subcritical Stein manifolds. Other applications include the Weinstein conjecture in certain product manifolds, obstructions to exact Lagrangian embeddings, existence of holomorphic curves with Lagrangian boundary condition, as well as symplectic capacities.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8d3334a48c4ea06ad6e00eb15952172bb4f4df38

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. J. Pardon
2. M. Abouzaid
3. Sheel Ganatra
4. P. Seidel
5. Vivek V. Shende
6. Mark McLean
7. D. Auroux
8. I. Smith

In Mathematical Physics

1. J. Pardon
2. M. Abouzaid
3. Sheel Ganatra
4. P. Seidel
5. Vivek V. Shende
6. Mark McLean
7. D. Auroux
8. I. Smith

Citations in the corpus

• Altering symplectic manifolds by homologous recombination (2010, background): “Since the symplectic cohomology of E vanishes by [43], Property 2.”
• Sectorial descent for wrapped Fukaya categories (2018, background): “0) = W(X;f 1). 1.2 Kunneth embedding Floer theory is generally well-behaved under taking products of symplectic manifolds and Lagrangian submanifolds, and this extends to the wrapped setting. Oancea [39] proved a Kunneth formula for symplectic cohomology of Liouville manifolds (see also Groman [31])”
• Lefschetz fibrations and symplectic homology (2007, methodology): “Proof By one of the applications of [21], we have that SH .”
• Symplectic cohomology and Viterbo's theorem (2013, background): “These groups are extremely difficult to compute, except when they vanish, but they are known to satisfy good formal properties, including a version of the Künneth theorem [66].”
• Symplectic homology as Hochschild homology (2006, unknown): “ar X iv :m at h/ 06 09 03 7v 4 [ m at h. SG ] 9 A pr 2 00 8 SYMPLECTIC HOMOLOGY AS HOCHSCHILD HOMOLOGY PAUL SEIDEL”