Green’s functions, Biot-Savart operators, and linking numbers on negatively curved symmetric spaces

Abstract

We construct radial fundamental solutions for the differential form Laplacian on negatively curved symmetric spaces. At least, one of these Green’s functions also yields a Biot-Savart operator, i.e., a right inverse of the exterior differential on closed forms with image in the kernel of the codifferential. Any Biot-Savart operator gives rise to a Gauss linking integral.