Topological aspects of ℤ/2ℤ eigenfunctions for the Laplacian on S²

2021/08/11 by Clifford Henry Taubes, Yingying Wu, Taubes, Clifford Henry +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2108.05017

openalex publication_date 2021/08/11 · openalex created_date 2021/08/16 · openalex updated_date 2026/07/28

Abstract

This paper concerns the behavior of the eigenfunctions and eigenvalues of the round sphere's Laplacian acting on the space of sections of a real line bundle which is defined on the complement of an even numbers of points in S². Of particular interest is how these eigenvalues and eigenvectors change when viewed as functions on the configuration spaces of points.

Citations

• The zero loci of Z/2 harmonic spinors in dimension 2, 3 and 4
• Extended Functorial Field Theories and Anomalies in Quantum Field Theories

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