Index theory of Dirac operators on manifolds with corners up to codimension two

In this expository article, we survey index theory of Dirac operators using the Gauss-Bonnet formula as the catalyst to discuss index formulas on manifolds with and without boundary. Considered in detail are the Atiyah-Singer and Atiyah-Patodi-Singer index theorems, their heat kernel proofs, and their generalizations to manifolds with corners of codimension two via the method of `attaching cylindrical ends’. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.