Elliptic genera, transgression and loop space Chern-Simons forms

• DOI: 10.4310/cag.2009.v17.n1.a4
• Publication Date: 2013-08-30T22:25:02Z
• Authors: Qingtao Chen; Fei Han
• Keywords: Mathematics - Differential Geometry; 53C20, 57R20, 53C80, 11Z05; Differential Geometry (math.DG); FOS: Mathematics; Algebraic Topology (math.AT); Mathematics - Algebraic Topology; 0101 mathematics; 01 natural sciences

some materials added<br/>We compute the Chern-Simons transgressed forms of some modularly invariant characteristic forms, which are related to the elliptic genera. We study the modularity properties of these secondary characteristic forms and the relations among them. We also compute the Chern-Simons forms of some vector bundles over free loop space.<br/>