Elliptic Genera, Transgression and Loop Space Chern-Simons Forms

2006/11/04 by Qingtao Chen, Chen, Qingtao, Fei Han +1
Mathematics · #11Z05 #53C20 #53C80 #57R20 #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #math.AT #math.DG #msc:11Z05 #msc:53C20 #msc:53C80 #msc:57R20

paper · pdf · doi:10.48550/arxiv.math/0611104

some materials added

arxiv created 2007/12/08 · arxiv updated 2009/12/01

Abstract

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.

Related

• Chern-simons forms on associated bundles, and boundary terms
• A loop group extension of the odd Chern character
• Modular forms via invariant theory
• The Geometry of Loop Spaces II: Characteristic Classes
• On transgression in associated bundles