几何拓扑研讨班：BNPC manifolds of dimension at most four are Euclidean

中国科学院数学与系统科学研究院

数学研究所

学术报告

几何拓扑研讨班

Speaker: 谷世杰 教授(东北大学）

Title: BNPC manifolds of dimension at most four are Euclidean

Time&Venue: 2024年11月12日（星期二）10:30-11:30 & 晨兴110

Abstract: In 1981, Gromov asked whether there exist simply connected topological manifolds, other than Euclidean space, that admit a metric of non-positive curvature in a synthetic sense. Since CAT(0) spaces are contractible, it follows from the classification of surfaces that any CAT(0) 2-manifold is Euclidean. In dimension 3, by combining results of Brown and Rolfsen, CAT(0) manifolds are homeomorphic to R^3. Recently, Lytchak, Nagano, and Stadler proved that CAT(0) 4-manifolds are Euclidean. In this talk, I will discuss Gromov's question and introduce spaces of (global) non-positive curvature in the sense of Busemann, abbreviated as BNPC spaces. I will show that the results above can be extended to BNPC manifolds. This is joint work with Tadashi Fujioka.