Cheeger-Chern-Simons Character: Definition, Applications & Significance

The Cheeger-Chern-Simons character, also known as the CCS character, is a mathematical object that arises in differential geometry and gauge theory. It is named after Jeff Cheeger, Shiing-Shen Chern, and James Simons, who made significant contributions to the study of this character.

In differential geometry, the CCS character is a topological invariant that captures information about the topology of a manifold. It is defined using the secondary characteristic classes, which are constructed from the first and second Chern classes of a vector bundle. The CCS character can be thought of as a higher-dimensional generalization of the Chern character.

In gauge theory, the CCS character plays a crucial role in understanding the quantization of certain gauge field theories. It is used to define the so-called Wess-Zumino-Witten models, which are two-dimensional quantum field theories with rich mathematical structure. The CCS character provides a way to compute the partition function of these models and study their topological properties.

Overall, the Cheeger-Chern-Simons character is a fundamental mathematical object that has applications in various areas of mathematics and physics. Its study has deepened our understanding of topology, geometry, and quantum field theory.