题目：Homological criteria for finite domination of chain complexes

　　报告人：Dr. Thomas Huettemann(Queen's University Belfast, United Kingdom)

　　Abstract: A chain complex of modules over a unital ring R is called R-finitely dominated if it is a retract up to homotopy (or: direct summand up to homotopy) of a bounded chain complex of finitely generated free R-modules. This notion has applications in group theory (eg, groups of type FP, Sigma-invariants of groups) and topology (eg, finiteness conditions for covering spaces, ends of manifolds). As a special case, I will discuss when a bounded complex of finitely generated free R[x,1/x]-modules is R-finitely dominated. There exists a beautiful characterisation of finite domination by vanishing of Novikov homology, and I will explain how naive algebraic geometry, suitably formulated, yields a rather transparent proof of the result. I will then explain how this approach can be combined with ideas from toric geometry to give a generalisation to the case of Laurent polynomial rings with several indeterminates; this might look like an easy exercise at first but leads to rather intriguing combinatorial and homological questions.

　　时间：2015年7月16日（周四）10:00-11:00

　　地点：首都师大北一区文科楼 707 教室

　　欢迎全体师生积极参加！