Speaker: 欧阳泽轩博士后，西湖大学

Inviter: 简旺键副研究员

Title: Positive Sectional Curvature on an Exotic Sphere

Language: Chinese

Time & Venue: 2026.09.29 09:00-10:00 腾讯会议：574-8078-3311

Abstract: The existence of metrics with positive sectional curvature on exotic spheres is a fundamental problem concerning the interaction between curvature and smooth structure. In this talk, I will discuss a construction of a positively curved metric on an exotic 7-sphere. The construction begins with a bi-invariant metric on Sp(2) and introduces an explicit deformation compatible with the relevant quotient structure. The main geometric problem is then reduced to the study of sectional curvature on horizontal two-planes. The argument combines the structure of the Lie algebra, the geometry of Riemannian submersions, and a detailed analysis of the behavior of curvature under the deformation. Special attention is given to the locus where the leading curvature contribution vanishes. By analyzing these locus more carefully and combining local curvature estimates with compactness, one obtains strict positivity of sectional curvature for sufficiently small deformation parameters.