论文标题
具有无限光谱规范的传奇人物和拉格朗日人的家庭
Families of Legendrians and Lagrangians with unbounded spectral norm
论文作者
论文摘要
维特尔博（Viterbo）猜想，在零段的hamiltonian同位素的圆环单位捆绑包中的任何拉格朗日都可以满足其光谱规范的均匀束缚； Shelukhin的最新结果表明确实如此。 The modest goal of this note is to explore two natural generalisations of the above geometric setting in which the bound of the spectral norm fails: first, passing to Legendrian isotopies in the contactisation of the unit co-disc bundle (Hamiltonian isotopies lift to Legendrian isotopies) and, second, considering Hamiltonian isotopies but after modifying the co-disc bundle by attaching a critical Weinstein one-handle.
Viterbo has conjectured that any Lagrangian in the unit co-disc bundle of a torus which is Hamiltonian isotopic to the zero-section satisfies a uniform bound on its spectral norm; a recent result by Shelukhin showed that this is indeed the case. The modest goal of this note is to explore two natural generalisations of the above geometric setting in which the bound of the spectral norm fails: first, passing to Legendrian isotopies in the contactisation of the unit co-disc bundle (Hamiltonian isotopies lift to Legendrian isotopies) and, second, considering Hamiltonian isotopies but after modifying the co-disc bundle by attaching a critical Weinstein one-handle.
