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 ${S}^2$. Of particular interest is how these eigenvalues and eigenvectors change when viewed as functions on the configuration spaces of points.
Funding Statement
C.H.T was supported in part by the National Science Foundation grant DMS 2002771.
Y.W. undertook the research reported here while affiliated with the Center of Mathematical Sciences and Applications at Harvard University.
Citation
C. H. Taubes. Y. Wu. "Topological aspects of $\mathbb{Z} / 2 \mathbb{Z}$ eigenfunctions for the Laplacian on $S^2$." J. Differential Geom. 128 (1) 379 - 462, September 2024. https://doi.org/10.4310/jdg/1721075265
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