Khovanov Homology, Exotic Planes, and Geometric Structures on Them
发布时间：2026年08月24日
浏览次数：11
发布者: He Liu
主讲人： 滕逸恺（Rutgers University）
活动时间： 从 2026-08-28 15:00 到 16:00
场地： 北京国际数学研究中心，全斋全29教室
Since the 1980s, mathematicians have discovered uncountably many "exotic" embeddings of R^2 in R^4, i.e., embeddings that are topologically but not smoothly isotopic to the standard xy-plane. However, until today, there have been no direct, computable invariants that could detect such exotic behavior (with prior results relying on indirect arguments). In this talk, we define the end Khovanov homology, which is the first known combinatorial invariant of properly embedded surfaces in R^4 up to ambient diffeomorphism. Moreover, we apply this invariant to detect new exotic planes, including the first known example of an exotic plane that is a Lagrangian submanifold of the standard symplectic R^4.
