Communications in Analysis and Geometry

Volume 17 (2009)

Number 1

Elliptic genera, transgression and loop space Chern-Simons forms

Pages: 73 – 106



Qingtao Chen (Department of Mathematics, University of California at Berkeley)

Fei Han (Department of Mathematics, Stanford University)


We compute the Chern-Simons transgressed forms of some characteristic forms with modular properties, which are related to 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.

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