A Poincaré-Hopf type formula for Chern character numbers
نویسندگان
چکیده
For two complex vector bundles admitting a homomorphism with isolated singularities between them, we establish a Poincaré-Hopf type formula for the difference of the Chern character numbers of these two vector bundles. As a consequence, we extend the original Poincaré-Hopf index formula to the case of complex vector fields.
منابع مشابه
Quantum double and κ-Poincaré symmetries in (2+1)-gravity and Chern-Simons theory
We review the role of Drinfeld doubles and κ-Poincaré symmetries in quantised (2+1)gravity and Chern-Simons theory. We discuss the conditions under which a given Hopf algebra symmetry is compatible with a Chern-Simons theory and determine this compatibility explicitly for the Drinfeld doubles and κ-Poincaré symmetries associated with the isometry groups of (2+1)-gravity. In particular, we expla...
متن کاملEquivariant K-theory, twisted Chern character, index pairings, Poincaré duality and orientation for the standard Podleś sphere
The noncommutative spin geometry of the standard Podleś sphere is analyzed and known results are extended by establishing Poincaré duality and orientability. In the discussion of orientability, Hochschild homology is replaced by a twisted version which avoids the dimension drop. The twisted Hochschild cycle representing an orientation is related to the volume form of the distinguished covariant...
متن کاملA theorem of Poincaré-Hopf type
We compute (algebraically) the Euler characteristic of a complex of sheaves with constructible cohomology. A stratified Poincaré-Hopf formula is then a consequence of the smooth Poincaré-Hopf theorem and of additivity of the Euler-Poincaré characteristic with compact supports, once we have a suitable definition of index. AMS classification: 55N33 57R25
متن کاملChern Character, Hopf Algebras, and Brs Cohomology
We present the construction of a Chern character in cyclic cohomology, involving an arbitrary number of associative algebras in contravariant or covariant position. This is a generalization of the bivariant Chern character for bornological algebras introduced in a previous paper [35], based on Quillen superconnections and heat-kernel regularization. Then we adapt the formalism to the cyclic coh...
متن کاملCyclic cohomology of Hopf algebras, and a non-commutative Chern-Weil theory
We give a construction of Connes-Moscovici’s cyclic cohomology for any Hopf algebra equipped with a character. Furthermore, we introduce a non-commutative Weil complex, which connects the work of Gelfand and Smirnov with cyclic cohomology. We show how the Weil complex arises naturally when looking at Hopf algebra actions and invariant higher traces, to give a non-commutative version of the usua...
متن کامل