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Minimal kernels of Dirac operators along maps

Wittmann, Johannes


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 D-g,h(f) of the twisted Dirac bundle Sigma M circle times(R)f(*)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 D-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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