拓扑研讨班：Rationalization theories for non-nilpotent spaces and groups

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：IVANOV SERGEI Professor (BIMSA)  

题  目：Rationalization theories for non-nilpotent spaces and groups

时  间：2023.05.24（星期三）14:30-16:30

地  点：数学院南楼N702

摘  要：We give an overview of five rationalization theories for non-nilpotent spaces (Bousfield–Kan’s Q-completion; Sullivan’s rationalization; Bousfield’s homology rationalization; Casacuberta– Peschke’sΩ-rationalization; G´omez-Tato–Halperin–Tanr´e’s π_1- fiberwise rationalization) that extend the classical rationalization of simply connected spaces. We also give an overview of the corresponding rationalization theories for groups (Q-completion; HQ-localization; Baumslag rationalization) that extend the classical Malcev completion. In addition, we will tell about our results on the rationalization of the wedge of two circles for all these types of rationalisations.  

个人简介：I defended my PhD thesis under the supervision of Alexander Generalov in 2013. I worked with him on Hochschild homology theory of finite dimensional algebras and its relation to representation theory. Then I started to work in collaboration with Roman Mikhailov on homological algebra and some relations between group theory and homotopy theory. I recently changed my field of study to “homotopy theory of graphs”: path homology and magnitude homology of digraphs.