Loading...

Hodge Structure on Fundamental Groups

Zeinali, Nima | 2017

1309 Viewed
  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 49587 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Jafari, Amir
  7. Abstract:
  8. Deligne Proved that cohomology groups of algebraic varieties over C have mixed Hodge structures.It is also proved that homotopy groups of these varieties have mixed Hodge structures in a proper sense.In this thesis using iterated integrals that introduced by Chen,we explain Hain’s approach for defining Hodge structures on truncated first homotopy groups(fundamental groups). Note that there is another approach for defining Hodge structures on homotopy groups by Morgan,that uses minimal models of Sullivan.For explaining Hain’s approach,some basic results on Hodge structures are also explained
  9. Keywords:
  10. Mixed Hodge Structure ; Iterated Integrals Renormalization ; Fundamental Group Representation ; Mixed Hodge Complex ; Torelli Theorem ; Harmonic Volume

 Digital Object List