Multiple period integrals and cohomology

Abstract

This work gives a version of the Eichler-Shimura isomorphism with a non-abelian $H^1$ in group cohomology. Manin has given a map from vectors of cusp forms to a noncommutative cohomology set by means of iterated integrals. We show Manin's map is injective but far from surjective. By extending Manin's map we are able to construct a bijective map and remarkably this establishes the existence of a non-abelian version of the Eichler-Shimura map.

References in corpus (1)

• Motivic periods and the projective line minus three points

Cited by in corpus (2)

• Multiple Dedekind Symbols
• Modular forms of real weights and generalized Dedekind symbols