Algebra & Number Theory

Multiple period integrals and cohomology

Roelof Bruggeman and Youngju Choie

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We give a version of the Eichler–Shimura isomorphism with a nonabelian H1 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 that 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 nonabelian version of the Eichler–Shimura map.

Article information

Algebra Number Theory, Volume 10, Number 3 (2016), 645-664.

Received: 29 June 2015
Revised: 26 February 2016
Accepted: 28 February 2016
First available in Project Euclid: 16 November 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols
Secondary: 11F75: Cohomology of arithmetic groups

cusp form iterated integral noncommutative cohomology


Bruggeman, Roelof; Choie, Youngju. Multiple period integrals and cohomology. Algebra Number Theory 10 (2016), no. 3, 645--664. doi:10.2140/ant.2016.10.645.

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