Unipotent Modules and the Bar-complex

Student: Nesterova Elizaveta

Supervisor: Sergey Gorchinskiy

Educational Programme: Mathematics (Bachelor)

Final Grade: 10

Year of Graduation: 2021

Let $M$ be a differentiable manifold, x \in M. Chen identified the coordinate ring of prounipotent completion of \pi_1(M,x) with H^0 of a certain complex associated to de Rham algebra of $M$, and Parshin's iterated integrals as a map \pi_1(M,x) to this H^0. The goal of this work lies in giving a general treatment of Chen's result for an arbitary augmented differential graded algebra.

Full text (added May 31, 2021)

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