Symplectic embeddings of four-dimensional polydisks into half integer ellipsoids

2020/10/13 by Leo Digiosia, Digiosia, Leo, J. M. Nelson +7 · 1 citation
Mathematics · Computer Science · #Finite Group Theory Research #Coding theory and cryptography #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2010.06687

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≤ a< 2 and b is a half-integer. When 1 ≤ a < 2-O(b^-1) we demonstrate that P(a,1) symplectically embeds into E(bc,c) if and only if a+b≤ bc. Our results show that inclusion is optimal and extend the result by Hutchings \citeH when b is an integer. Our proof is based on a combinatorial criterion developed by Hutchings \citeH to obstruct symplectic embeddings.

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• Refined Elementary Capacities from Symplectic Field Theory

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