Abstract:In this talk I will briefly present the historical development behind Chern's proof in 1944 of the higher dimensional Gauss-Bonnet formula, starting with the work of H. Hopf back in 1925. I will then introduce the notion of double forms (which basically are sums of tensor products of differential forms) and explain how these tensors help us reformulate the Gauss-Bonnet-Chern-Formula a...
AbstractWe review general results of N=2 supersymmetric localization on non singular 3-manifolds(closed, oriented). In specific, review the general philosophy and collect some formulae which frequently appear in other contexts involving 3d supersymmetric partition functions. We discuss some generalization to singular manifolds or 3-manifolds with boundary (for example, a half index)