A super-twisted Dirac operator and Novikov inequalities
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A super-twisted Dirac operator is constructed and deformed suitably. Following Shubin’s approach to Novikov inequalities associated to the deformed de Rham-Hodge operator, we give a for mula for the index of the super-twisted Dirac operator, and Novikov type inequalities for the deformed operator. In particular, we obtain a purely analytic proof of the Hopf index theorem for general vector bundles.
Keywordssuper-twisted Dirac operator Hopf index theorem Novikov inequalities
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