TL;DR
This paper advances the understanding of iterated integrals of modular forms by describing their cohomology and cocycle images, building on prior work with a focus on Shimura integrals and symbols.
Contribution
It provides a new description of iterated Shimura cohomology and characterizes the image of the iterated Shimura cocycle class, extending previous research on modular symbols.
Findings
Description of iterated Shimura cohomology
Characterization of the cocycle class image
Review of classical modular symbols and open problems
Abstract
In this paper I continue the study of iterated integrals of modular forms and noncommutative modular symbols for started in [Ma3]. Main new results involve a description of the iterated Shimura cohomology and the image of the iterated Shimura cocycle class inside it. The concluding section of the paper contains a concise review of the classical modular symbols for SL(2) and a discussion of open problems.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Finite Group Theory Research