Iterated Integrals and Periods of Algebraic Fundamental Groups

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Heidarzadeh, Leila | 2012

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 42810 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Jafari, Amir
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
Keywords:
Iterated Integrals Renormalization ; Normalization ; Mixed Hodge Structure ; Shuffle Relations ; Hopf Algebra ; Mixed Hodge Theory ; Framed Mixed Hadge-Tate Structure

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