From Riemannian determinants to Taylor-fibration

M. K. Chiang
Comments: 8 pages, 3 figures. To appear in the proceedings for the conference "Theories of Higher Dimensions", held at the Institute of Higher Dimensions, Monterrey, Mexico, Maynooth, Ireland, November 2017

We give a definition of determinants as sums that relate variables of positions and boundary conditions. We implement this definition in the context of Riemannian determinants, which are non-compact spaces. We obtain a formula for determinants from the Taylor-fibration formula that we compute in the context of Riemannian determinants. This formula is a K-theory formula for determinants. We prove that the formula of determinants is an exact formula for the determinants of a determinant whose position is fixed by a single element of the determinants of the determinant. Finally, we demonstrate how the Taylor-fibration formula simplifies the implementation of determinants.