## Algebra & Number Theory

### Multiple period integrals and cohomology

#### Abstract

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

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

Dates
Revised: 26 February 2016
Accepted: 28 February 2016
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.ant/1510842498

Digital Object Identifier
doi:10.2140/ant.2016.10.645

Mathematical Reviews number (MathSciNet)
MR3513133

Zentralblatt MATH identifier
1346.11034

#### Citation

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. https://projecteuclid.org/euclid.ant/1510842498

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