Geodesic
Equivariant Brill–Noether theory for elliptic operators and superrigidity of J-holomorphic maps
Forum of Mathematics, Sigma, Tome 11 (2023)

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The space of Fredholm operators of fixed index is stratified by submanifolds according to the dimension of the kernel. Geometric considerations often lead to questions about the intersections of concrete families of elliptic operators with these submanifolds: Are the intersections nonempty? Are they smooth? What are their codimensions? The purpose of this article is to develop tools to address these questions in equivariant situations. An important motivation for this work are transversality questions for multiple covers of J-holomorphic maps. As an application, we use our framework to give a concise exposition of Wendl’s proof of the superrigidity conjecture. 
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     author = {Aleksander Doan and Thomas Walpuski},
     title = {Equivariant {Brill{\textendash}Noether} theory for elliptic operators and superrigidity of {J-holomorphic} maps},
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Aleksander Doan; Thomas Walpuski. Equivariant Brill–Noether theory for elliptic operators and superrigidity of J-holomorphic maps. Forum of Mathematics, Sigma, Tome 11 (2023). doi: 10.1017/fms.2022.104

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