Minimal kernels of Dirac operators along maps | Zendy

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Minimal kernels of Dirac operators along maps

Author(s) -

Wittmann Johannes

Publication year - 2019

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.201800069

Subject(s) - dirac operator , mathematics , clifford analysis , manifold (fluid mechanics) , dirac (video compression format) , dimension (graph theory) , upper and lower bounds , riemannian manifold , operator (biology) , pure mathematics , index (typography) , dirac algebra , atiyah–singer index theorem , mathematical analysis , mathematical physics , dirac equation , physics , quantum mechanics , computer science , mechanical engineering , biochemistry , chemistry , repressor , neutrino , transcription factor , engineering , gene , world wide web

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 operatorD ̸ g , h f of the twisted Dirac bundle Σ M ⊗ R f ∗ TN . To this Dirac operator one can associate an index inKO − dim ( M )( pt ) . If M is 2‐dimensional, one gets a lower bound for the dimension of the kernel ofD ̸ g , h f out of this index. We investigate the question whether this lower bound is obtained for generic tupels ( f , g , h ) .

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