Essential tori in spaces of symplectic embeddings

Chaidez, Julian; Munteanu, Mihai

doi:10.2140/agt.2021.21.2489

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Essential tori in spaces of symplectic embeddings

Julian Chaidez and Mihai Munteanu

Algebraic & Geometric Topology 21 (2021) 2489–2522

DOI: 10.2140/agt.2021.21.2489

Abstract

Given two $2 n$ –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

References

Publication

Received: 11 December 2019

Revised: 3 August 2020

Accepted: 14 November 2020

Published: 31 October 2021

Authors

Julian Chaidez
Department of Mathematics University of California, Berkeley Berkeley, CA United States
http://www.math.berkeley.edu/~jchaidez
Mihai Munteanu
Mathematics Department Humboldt-Universitat zu Berlin Berlin Germany

Volume 21, issue 5 (2021)