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shuffle-relations
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Iterated Integrals and Periods of Algebraic Fundamental Groups
, M.Sc. Thesis Sharif University of Technology ; Jafari, Amir (Supervisor)
Abstract
In This thesis, we study first the analytic properties of Iterated integrals on complex line and discuss their shuffle relations and also regularization for divergent integrals, Next we turn in to Mixed Hodge theory and define a Hopf algebra of framed Mixed Hodge -Tate Structures. Associated to any iterated integral ∫ an+1 a0 dt ta1 dt ta2 ::: dttan
we define an n-framed Mixed Hodge-Tate structure denoted by IH(a0; a1; :::; an; an+1) . These structure come from the fundamental group of Cfa1; :::; ang and for this we recall the theory of Chen and Hain for these groups. At the end calculate a coproduct formula for these elements
we define an n-framed Mixed Hodge-Tate structure denoted by IH(a0; a1; :::; an; an+1) . These structure come from the fundamental group of Cfa1; :::; ang and for this we recall the theory of Chen and Hain for these groups. At the end calculate a coproduct formula for these elements