论文标题
四维多功能的四个周期无限楼梯
Four-periodic infinite staircases for four-dimensional polydisks
论文作者
论文摘要
符号四序列的椭圆形嵌入函数测量必须缩放其符号形式的数量，以便它允许嵌入不同偏心率的椭圆形的嵌入。此功能概括了Gromov宽度和球填充号码。在一个经过分析的一个符合性的四个manifolds家族中，对复杂的投影平面的单点爆炸，有一组开放的浓密象征性形式，其椭圆形嵌入功能完全有限地描述了许多障碍物，而同时存在的cantor形式是一组cantor cantor semplectic see for tern tern tern tern tern tern tern tern Infininities nucfininite nefininite she Infininite nubininite she Infininite nubininite n s a noce nefininite she Infininite se n s a infininite n s a infininity中均有限的障碍物。在后一种情况下，我们说嵌入功能具有无限的楼梯。在本文中，我们确定了一个新的无限楼梯时，当目标是四维多磁道时，扩展了usher在2019年确定的可数家族。我们的工作在无限的许多间隔上计算功能，从而指示了usher的猜想的证明方法。
The ellipsoid embedding function of a symplectic four-manifold measures the amount by which its symplectic form must be scaled in order for it to admit an embedding of an ellipsoid of varying eccentricity. This function generalizes the Gromov width and ball packing numbers. In the one continuous family of symplectic four-manifolds that has been analyzed, one-point blowups of the complex projective plane, there is an open dense set of symplectic forms whose ellipsoid embedding functions are completely described by finitely many obstructions, while there is simultaneously a Cantor set of symplectic forms for which an infinite number of obstructions are needed. In the latter case, we say that the embedding function has an infinite staircase. In this paper we identify a new infinite staircase when the target is a four-dimensional polydisk, extending a countable family identified by Usher in 2019. Our work computes the function on infinitely many intervals and thereby indicates a method of proof for a conjecture of Usher.
