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arXiv · 1512.06225

Multiple period integrals and cohomology

Roelof Bruggeman·YoungJu Choie
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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.

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Roelof Bruggeman, YoungJu Choie. 2015-12-19. Multiple period integrals and cohomology. https://doi.org/10.2140/ant.2016.10.645

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