Abstract
We give a version of the Eichler–Shimura isomorphism with a nonabelian 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 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.
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.
| Original language | English |
|---|---|
| Pages (from-to) | 645-664 |
| Number of pages | 20 |
| Journal | Algebra Number Theory |
| Volume | 10 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 17 Jun 2016 |
Bibliographical note
Published online June 17, 2016Keywords
- cusp form
- iterated integral
- noncommutative cohomology