An integral Riemann-Roch theorem for surface bundles

TL;DR

This paper establishes an integral version of the Riemann-Roch theorem specifically for surface bundles, linking classical cohomology classes with those derived from the symplectic group.

Contribution

It introduces an integral Riemann-Roch theorem for surface bundles, extending classical results to an integral setting and connecting cohomology with symplectic group classes.

Findings

Proves an integral Riemann-Roch theorem for surface bundles.

Establishes a relationship between standard and symplectic cohomology classes.

Advances understanding of surface bundle cohomology in an integral framework.

Abstract

This paper proves an integral version of the Riemann-Roch theorem for surface bundles, comparing the standard cohomology classes with the cohomology classes coming from the symplectic group.