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

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.

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spaces of symplectic embeddings, symplectic field theory, ellipsoids, holomorphic cylinders
Mathematical Subject Classification 2010
Primary: 53D05, 53D42, 58D10
Received: 11 December 2019
Revised: 3 August 2020
Accepted: 14 November 2020
Published: 31 October 2021
Julian Chaidez
Department of Mathematics
University of California, Berkeley
Berkeley, CA
United States
Mihai Munteanu
Mathematics Department
Humboldt-Universitat zu Berlin