Essential tori in spaces of symplectic embeddings

Abstract

Given two $2n$--dimensional symplectic ellipsoids whose symplectic sizes satisfy certain inequalities, we show that a certain map from the $n$--torus to the space of symplectic embeddings from one ellipsoid to the other induces an injective map on singular homology with mod $2$ coefficients. The proof uses parametrized moduli spaces of $J$--holomorphic cylinders in completed symplectic cobordisms.

32 pages. Comments welcome!

References in corpus (3)

• Lectures on Symplectic Field Theory
• Symplectic capacities from positive S^1-equivariant symplectic homology
• The ghost stairs stabilize to sharp symplectic embedding obstructions