Instantons on multi-Taub-NUT Spaces I: Asymptotic Form and Index Theorem

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We study finite action anti-self-dual Yang-Mills connections on the multi-Taub-NUT space. We establish the curvature and the harmonic spinors decay rates and compute the index of the associated Dirac operator. This is the first in a series of papers proving the completeness of the bow construction of instantons on multi-Taub-NUT spaces and exploring it in detail.





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Cherkis, Sergey A, Andres Larrain-Hubach and Mark Stern (2019). Instantons on multi-Taub-NUT Spaces I: Asymptotic Form and Index Theorem. Journal of Differential Geometry, 119(1). pp. 1–72. 10.4310/jdg/1631124166 Retrieved from

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Mark A. Stern

Professor of Mathematics

The focus of Professor Stern's research is the study of analytic problems arising in geometry, topology,  physics, and number theory.

In recent work, Professor Stern has studied analytical, geometric, and topological questions arising from Yang-Mills theory, Hodge theory, and number theory. These have led for example to a study of (i) stability questions arising in Yang Mills theory and harmonic maps, (ii) energy minimizing connections and instantons,  (iii) new bounds for eigenvalues of Laplace Beltrami operators, and (iv) new bounds for betti numbers.

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