The authors generalize the works in [5] and [6] to prove a Hopf index theorem associated to a smooth section of a real vector bundle with non-isolated zero points.
A s黳er-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 supe...A s黳er-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.展开更多
This paper presents a definition of residue formulas for the Euler class of cohomology-oriented sphere fibrations ξ. If the base of ξ is a topological manifold, a Hopf index theorem can be obtained and, for the smoo...This paper presents a definition of residue formulas for the Euler class of cohomology-oriented sphere fibrations ξ. If the base of ξ is a topological manifold, a Hopf index theorem can be obtained and, for the smooth category, a generalization of a residue formula is derived for real vector bundles given in [2].展开更多
文摘The authors generalize the works in [5] and [6] to prove a Hopf index theorem associated to a smooth section of a real vector bundle with non-isolated zero points.
文摘A s黳er-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.
基金Project supported by the DGICYT Grant (No. MTM2007-60016)the Junta de Andalucía Grant(No. P07-FQM-2863)
文摘This paper presents a definition of residue formulas for the Euler class of cohomology-oriented sphere fibrations ξ. If the base of ξ is a topological manifold, a Hopf index theorem can be obtained and, for the smooth category, a generalization of a residue formula is derived for real vector bundles given in [2].
