A Riemann-Roch-Grothendieck theorem for flat fibrations with complex fibers

作者：Zhang Yeping^*

来源：Comptes Rendus Mathematique, 2016, 354(4): 401-406.

DOI：10.1016/j.crma.2016.01.011

We consider a proper flat fibration with real base and complex fibers. First we construct odd characteristic classes for such fibrations by a method that generalizes constructions of Bismut-Lott [5]. Then we consider the direct image of a fiberwise holomorphic vector bundle, which is a flat vector bundle on the base. We give a Riemann-Roch-Grothendieck theorem calculating the odd real characteristic classes of this flat vector bundle.

• 出版日期2016-4