中科院数学与系统科学研究院

数学研究所

中科院华罗庚数学重点实验室

综合报告会

（Colloquium）

报告人：Prof. Donald Stanley（University of regina）

题  目：Configuration spaces

时  间：09.25 (星期四), 15:00--16:00

地  点：数学院南楼N913室

Abstract：If $M$ is a manifold (or even a topological space), the configuration space $F(M,k)$ is the space of $k$ distinct ordered points in $M$. For example, the space $F(\mathbb R^3,k)$ represents the space of possible configurations of $k$ objects in space. First we consider the special case of $F(\mathbb R^2, k)$ and describe its cohomology and homotopy groups, and its connection with the braid group $P_k$. We then move on to discuss the following two actively researched problems:

1) When is $F(M,k)$ invariant under homotopy?
2) Find an algebraic model for $F(M,k)$.
The present research is joint work with Pascal Lambrechts.