Title：Combinatorial Gauss-Bonnet theorem and the Alexander-Spanier cohomology 

Speaker：Hitoshi Moriyoshi (Nagoya university)

Time：2018年9月7日（周五）    下午 16:00-17:30

Room：东区管理科研楼   数学科学学院1418室

Abstract：For a smooth surface the celebrated Gauss-Bonnet theorem tells that the integration of the Gauss curvature is equal to the Euler number of surface times 2/pi. Also on a combinatorial surface, namely a polyhedral surface, there is a similar theorem to the above, that is, the sum of Angle defect at each vertex amounts to the Euler number of surface times 2/pi. This theorem goes back at least as far as Descartes. Thus the Angle defect seems to be a counterpart of the Gauss curvature on a polyhedral surface. In this talk we justify it by introducing a notion of the Alexander-Spanier cohomology, which also make possible a generalization of the theorem in higher dimensional case. The main subjects in my talk are polyhedrons, which are definitely accessible for everyone.