The order complex of cosets in a finite group

Abstract: 

In this talk, we will introduce some algebraic topology methods on studying the poset(=partial 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 divisi[1]bility 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、2020年度上海市引智人才XSC计划，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。