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An \(L^2\)-Index Formula for Monopoles with Dirac-Type Singularities

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Abstract

We prove the Fredholmness of the Dirac operators associated to monopoles with Dirac-type singularities on any complete oriented 3-dimensional Riemannian manifolds. We also calculate their \(L^2\)-indices.

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Acknowledgements

I am deeply grateful to my supervisor Takuro Mochizuki for insightful and helpful discussions and advices. I thank Tsuyoshi Kato for kindly answering to my question about the \(S^1\)-equivariant index theorem. I also thank the referees for careful reading and giving useful comments.

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  1. Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan

    Masaki Yoshino

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  1. Masaki Yoshino
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Correspondence to Masaki Yoshino.

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Communicated by N. Nekrasov

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Yoshino, M. An \(L^2\)-Index Formula for Monopoles with Dirac-Type Singularities. Commun. Math. Phys. 375, 1811–1832 (2020). https://doi.org/10.1007/s00220-019-03574-6

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  • DOI: https://doi.org/10.1007/s00220-019-03574-6

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