Appears in collection : Not Only Scalar Curvature Seminar

In this talk, I will present a proof of a stable algebraic version of Gromov’s angle shrinking problem, and explain its application to our proof of Gromov’s dihedral rigidity conjecture. In particular, I will explain how it is used in our computation of the Fredholm index of the Dirac type operators on manifolds with polyhedral boundary. This talk is based on joint work with Zhizhang Xie and Guoliang Yu.