#### Volume 21, issue 5 (2021)

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Essential tori in spaces of symplectic embeddings

### Julian Chaidez and Mihai Munteanu

Algebraic & Geometric Topology 21 (2021) 2489–2522
##### 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.

##### Keywords
spaces of symplectic embeddings, symplectic field theory, ellipsoids, holomorphic cylinders
##### Mathematical Subject Classification 2010
Primary: 53D05, 53D42, 58D10