双极表面到大月鸟迹的索引

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2024-11-13 DOI:10.1007/s11040-024-09494-9

Egor Morozov

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引用次数: 0

摘要

对于每一个有理数（p/q 在 (1/2,\sqrt{2}/2)），我们都可以在（\mathbb {S}^1\）中构造一个 \(\mathbb {S}^3\)-后变的最小环，称为大月环，用 \(O_{p/q}\) 表示。将劳森双极面构造应用于 \(O_{p/q}/)可以得到 \(\mathbb {S}^4\) 中的最小环 \(\widetilde{O}_{p/q}/)。本文给出了 p/q 接近（（sqrt{2}/2）时这些环的莫尔斯指数和无效性的上下限。我们还提出了一个关于一般情况的数值猜想。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Index of Bipolar Surfaces to Otsuki Tori

For each rational number \(p/q\in (1/2,\sqrt{2}/2)\) one can construct an \(\mathbb {S}^1\)-equivariant minimal torus in \(\mathbb {S}^3\) called Otsuki torus and denoted by \(O_{p/q}\). The Lawson’s bipolar surface construction applied to \(O_{p/q}\) gives a minimal torus \(\widetilde{O}_{p/q}\) in \(\mathbb {S}^4\). In this paper we give upper and lower bounds on the Morse index and the nullity of these tori for p/q close to \(\sqrt{2}/2\). We also state a numerically assisted conjecture concerning the general case.

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来源期刊

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.