Anchored symplectic embeddings
Symplectic Geometry
2025-12-09 v2
Abstract
Given two four-dimensional symplectic manifolds, together with knots in their boundaries, we define an ``anchored symplectic embedding'' to be a symplectic embedding, together with a two-dimensional symplectic cobordism between the knots (in the four-dimensional cobordism determined by the embedding). We use techniques from embedded contact homology to determine quantitative critera for when anchored symplectic embeddings exist, for many examples of toric domains. In particular we find examples where ordinarily symplectic embeddings exist, but they cannot be upgraded to anchored symplectic embeddings unless one enlarges the target domain.
Cite
@article{arxiv.2407.08512,
title = {Anchored symplectic embeddings},
author = {Michael Hutchings and Agniva Roy and Morgan Weiler and Yuan Yao},
journal= {arXiv preprint arXiv:2407.08512},
year = {2025}
}
Comments
30 pages, 3 figures. Revised according to referee report