On the Ring Structure of Spark Characters
نویسنده
چکیده
We give a new description of the ring structure on the differential characters of a smooth manifold via the smooth hyperspark complex. We show the explicit product formula, and as an application, calculate the product for differential characters of the unit circle. Applying the presentation of spark classes by smooth hypersparks, we give an explicit construction of the isomorphism between groups of spark classes and the (p, p) part of smooth Deligne cohomology groups associated to a smooth manifold. We then give a new direct proof that this is an isomorphism of ring structures.
منابع مشابه
D-bar Sparks
A ∂-analogue of differential characters for complex manifolds is introduced and studied using a new theory of homological spark complexes. Many essentially different spark complexes are shown to have isomorphic groups of spark classes. This has many consequences: It leads to an analytic representation of O-gerbes with connection, it yields a soft resolution of the sheaf O by currents on the man...
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A ∂-analogue of differential characters for complex manifolds is introduced and studied using a new theory of homological spark complexes. Many essentially different spark complexes are shown to have isomorphic groups of spark classes. This has many consequences: It leads to an analytic representation of O ×-gerbes with connection, it yields a soft resolution of the sheaf O × by currents on the...
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