Elliptic genera, transgression and loop space Chern-Simons forms

Abstract

Connections in vector bundles play a very important role in differential geometry. The famous Chern–Weil theory relates connections to the theory of characteristic classes, which provides a geometric way to understand characteristic classes and therefore play a fundamental role in global differential geometry. Let ∇ be a connection on an n-dimensional real or complex vector bundle E → M , where M is a compact smooth manifold. The basic