走向现代数学学术报告 - 孟沆洋副教授（No. 655）

题目：The order complex of cosets in a finite group

报告人：孟沆洋 副教授（上海大学）

时间：2023年11月9日，16:00

地点：东海岸校区E209

摘要：In this talk, we will introduce some algebraic topology methods on studying the poset(=partially ordered set) of some cosets of a finite group. Let G be a finite group and X be a subgroup of G. We investigate the topological properties of poset C_X(G) of cosets Hx in G with X ≤ H < G. We show that C_X(G) is non-contracitble if G is solvable or N_G(X) contains a Sylow 2-subgroup and a Sylow 3-subgroup of G. This result follows J. Shareshian and R. Woodroofe’s work in Adv. Math(2016). We also gives some divisibility properties of the Euler characteristic of C_X(G) when X is a p-group, which follows K. S. Brown’s classical result in J.Algebra(2000).

报告人简介：孟沆洋，上海大学理学院数学系副教授。主要研究领域为有限群论及其表示，相关结果发表于Trans. Amer. Math. Soc., J. Lond. Math. Soc.，Proc. Amer. Math.Soc.，J. Algebra等杂志。获上海市2020年度扬帆计划项目，2021年获 Baer Prize特别提名奖，主持国家自然科学基金青年项目一项。