Categories,geometric groups and loop sp
发布单位: 科研处 发布时间: [2016-12-12] 浏览次数：
报告时间：2016-12-13 上午九点
报告地点：数理化楼A210
报告人：SONG, YONGJIN (宋庸鎭)
主办单位：数学学院
报告人简介：
SONG, YONGJIN (宋庸鎭), Professor, Department of Mathematics, Inha University, Vice President of Korean Mathematical Society (KMS),Chairman of Korean Mathematical Olympiad Committee. Research area: Algebraic Topology. His research interests are Category theory and homotopy theory, Loop space structures, Braid groups, Mapping class groups and Artin groups.Y. Song has organized many conferences including Daewoo Workshop on Pure Math., Korea-Japan Conference on Algebraic Topology, CJK(China-Japan-Korea) Conference on Algebraic Topology, East Asian Conference on Algebraic Topology, ICM Satellite Conference. KMS Topology Workshop.
报告内容简介：
The classifying space of a (braided) monoidal category induces a (double) loop space up to homotopy. The collection of some geometric groups gives rise to a braided monoidal category, therefore generates a double loop space structure. The braid structures inside mapping class groups can be explicitly expressed in terms of self-homomorphisms on the fundamental groups and also in terms of Dehn twists. There are various embeddings of braid groups into mapping class groups. We explain why those embeddings induce trivial homomorphim on homology groups. Here, the construction of a monoidal 2-category plays a key role. In this talk I will also introduce further embedding problems of Artin groups into mapping class groups.
