报告题目：On spaces realized as classifying spaces

主 讲 人：刘秀贵教授

报告时间：2024/10/24 周四上午10:00—12:00

报告邀请人：王咏乔

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报告摘要：In this talk, we will first recall some facts in rational homotopy theory and some results about the classifying space $Baut_1(X)$. Secondly, we will show that under some conditions non-trivial rank two rational spaces can not be realized as the classifying space of any $n$-connected, $\pi$-finite rational space, where $n\geq 1$. We will also show that if Eilenberg-MacLane space $K(\Q^r, n)$ $(r\geq 2,n\geq 2)$ can be realized as the classifying space of a simply connected elliptic rational space $X$, then $X$ has the rational homotopy type of $\prod_{r} S^{n-1}$ with $n$ even. This is joint work with Y. Bai and S. Xie.

个人简历：刘秀贵，南开大学数学科学学院教授，博士生导师。主要从事代数拓扑方面的研究工作，在球面稳定同伦群和有理同伦论等方面取得了一系列研究成果，在《Algebraic and Geometric Topology》、《Topology and its Applications》、《Proceedings of the American Mathematical Society》等数学期刊发表论文40余篇。曾主持多项国家自然科学基金项目和教育部新世纪优秀人才支持计划项目。