Full Ellipsoid Embeddings and Toric Mutations

Abstract

This article introduces a new method to construct volume-filling symplectic embeddings of 4-dimensional ellipsoids by employing polytope mutations in toric and almost-toric varieties. The construction uniformly recovers the full sequences for the Fibonacci Staircase of McDuff-Schlenk, the Pell Staircase of Frenkel-Muller and the Cristofaro-Gardiner-Kleinman's Staircase, and adds new infinite sequences of ellipsoid embeddings. In addition, we initiate the study of symplectic tropical curves for almost-toric fibrations and emphasize the connection to quiver combinatorics.

arXiv comment57 Pages, 28 Figures. Mistake in Subsection 4.1 found that directly affects Theorem 1.8 and consequently part of the proof of Theorem 1.4. Theorem 1.8 cannot hold in the stated generality; we thank Dusa McDuff for finding this error. We are working on correcting it