Index Theory on Incomplete Cusp Edge Spaces

Abstract

We study Dirac-type operators on incomplete cusp edge spaces with invertible boundary families. In particular, we construct the heat kernel for the associated Laplace-type operator and prove that the Dirac operators are essentially self-adjoint and Fredholm on their unique self adjoint domain. Using the asymptotics of the heat kernel and a generalisation of Getzler's rescaling argument we establish an index formula for these operators including a signature formula for the Hodge-de Rham operator on Witt incomplete cusp edge spaces.