Minimal kernels of Dirac operators along maps

Johannes Wittmann

Mathematische Nachrichten, 2019, vol. 292, issue 7, 1627-1635

Abstract: Let M be a closed spin manifold and let N be a closed manifold. For maps f:M→N and Riemannian metrics g on M and h on N, we consider the Dirac operator D̸g,hf of the twisted Dirac bundle ΣM⊗Rf∗TN. To this Dirac operator one can associate an index in KO−dim(M)(pt). If M is 2‐dimensional, one gets a lower bound for the dimension of the kernel of D̸g,hf out of this index. We investigate the question whether this lower bound is obtained for generic tupels (f,g,h).

Date: 2019
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https://doi.org/10.1002/mana.201800069

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