Wednesday, October 16th, 2013
3:00pm - 4:00pm, in McCormack 1-417

Rita Jimenez Rolland

Northeastern University

Stability phenomena in cohomology

Abstract: Given a sequence of topological spaces Xn we associate a sequence of rational vector spaces Hi(Xn;Q): the ith rational cohomology group of Xn. We will discuss how these spaces change as the parameter n grows. In particular, we will consider the configuration space of n ordered and unordered points in the plane to illustrate two possible situations. In the first case (unordered configurations) we will see that the dimension of the vector spaces is eventually constant. On the other hand, in the second case (ordered configurations) we will understand how the symmetries of the space explain another stability phenomenon.