CHERN-SIMONS FORMS AND THOM FORMS AS ITERATED INTEGRALS

Abstract

In this thesis we discuss Chen's iterated integral theory and its important role as a bridge between cyclic homology and equivariant differential forms on free loop spaces. Based on the equivariant Chern character in cyclic bar complexes constructed by Getzler, Jones and Petrack, we introduce Güneysu-Ludewig's construction of the equivariant Chern-Simons transgressed form and show its relation to the Bismut-Chern-Simons form on free loop spaces under the iterated integral map. We also discuss some possible candidates which could be sent to the Thom form on free loop spaces by the iterated integral map.