Mini course| Institute of Mathematical Sciences
Time: Wednesday, September 11th、18th、25th, 2024 , 13:30-15:00
Location：IMS, RS408
Speaker: Xiaolei Wu, Fudan University
Abstract: In this lecture series, I shall discuss finiteness properties of groups. In the first lecture, I will discuss the basic definitions and theorems, including type F_n, type FP_n and their relations, and homological dimension, geometric dimension and their relations. In the second lecture, I will discuss the Bestvina-Brady Morse theory. In particular, how one can use this to construct examples of groups that are of type F_n but not F_{n-1}, groups that are of type FP_2 but not of F_2. In the third lecture, I will discuss Bieri-Neumann-Strebel’s theory of Sigma invariants. This theory can be used to determine the finiteness properties of subgroups of a given group lies between the commutator subgroup and the whole group.