Minseong Kwon, Integrability of G-structures II

This is a working seminar to introduce the notion of an integrable G-structure and its obstruction class. In the first talk, I discussed the definition of an integrable G-structure and introduced the existence theorem for the structure tensor. In this talk, I will construct the structure tensor of a G-structure, and then prove that the structure tensor is indeed an obstruction class of the integrability which is lying in the Spencer cohomology group. The main reference is the paper ‘The Integrability Problem for G-structures’ (1965) written by Victor Guillemin.