Abstract:

The Kervaire invariant problem asks in which dimensions there exits framed manifolds of Kervaire invariant one. This has many implications in geometry and topology, such as the classification of homotopy spheres. By efforts of Browder, Barratt, Jones, Mahowald, Tangora, Hill, Hopkins, Ravenel, we know the answers in dimensions other than 126. Recently, joint with Weinan Lin and Zhouli Xu, we show that there exists Kervaire invariant one manifolds in dimension126. Hence we can conclude that the only dimensions admitting framed manifolds of Kervaire invariant one are 2, 6, 14, 30, 62 and 126.

Bio:

Guozhen Wang is a Professor in Fudan University. His research focuses on developing practical methods in understanding homotopy groups.