Integral Riemann–Roch formulae for cyclic subgroups of mapping class groups

Abstract

ABSTRACT. The first author conjectured certain relations for Morita-Mumford classes and Newton classes in the integral cohomology of mapping class groups (integral Riemann-Roch formulae). In this paper, the conjecture is verified for cyclic subgroups of mapping class groups.

Periodicity for Mumford–Morita–Miller Classes of Surface Symmetries

“…MMM classes of surface symmetries were studied in [1,3,4,13,20]. In case G is a finite cyclic group, Uemura proved, among other things, a certain kind of periodicity for MMM classes of surface symmetries [20 T. Akita: Department of Mathematics, Hokkaido University, Sapporo, 060-0810 Japan; e-mail: akita@math.sci.hokudai.ac.jp T. Akita Theorem 1.1 (Uemura).…”