Symplectic embeddings of four-dimensional polydisks into half integer ellipsoids

Abstract

We obtain new sharp obstructions to symplectic embeddings of four-dimensional polydisks P(a, 1) into four-dimensional ellipsoids E(bc, c) when $$1\le a< 2$$ and b is a half-integer. When $$1 \le a < 2-O(b^{-1})$$ we demonstrate that P(a, 1) symplectically embeds into E(bc, c) if and only if $$a+b\le bc$$ . Our results show that inclusion is optimal and extend the result by Hutchings (Geom Topol 20(2):1085–1126, 2016) when b is an integer. Our proof is based on a combinatorial criterion developed by Hutchings [14] to obstruct symplectic embeddings.