中科院数学与系统科学研究院
数学研究所
学术报告
拓扑研讨班
报告人：段智鹏 （南京师范大学）
题 目：Vanishing lines and periodicities in higher real K-theories
时 间：2024.06.12（星期三）10:00-11:00
地 点：数学院南楼N602
摘 要：Higher real K-theories generalize topological K-theory, reflecting the beautiful periodic phenomena of stable homotopy groups of spheres and detecting numerous important elements within. In this talk, I will demonstrate that the homotopy fixed point spectral sequences, which compute their homotopy groups, exhibit strong horizontal vanishing lines. I will present the concrete filtration of these vanishing lines. Additionally, I will discuss the periodicities of these higher real K-theories, which can be viewed as a generalization of the Bott periodicity of KO at higher heights. This talk is based on joint work with Mike Hill, Guchuan Li, Xiaolin Danny Shi, Guozhen Wang, and Zhouli Xu.