Representation theory and homological stability |
Abstract: Homological stability is the remarkable phenomenon where for certain sequences X_n of groups or spaces -- e.g. the special linear group SL(n,Z), the braid group B_n, or the moduli space M_n of genus n Riemann surfaces -- the homology groups H_i(X_n) do not depend on n once n is large enough. But for many analogous sequences, from pure braid groups to congruence matrix groups to Torelli groups, homological stability fails horribly, and H_i(X_n) blows up to infinity. In many of these cases we know very little concretely about H_i(X_n), and it's possible there is no nice "closed form" for the answers. |
Web page: Alexandru I. Suciu | Comments to: andrei@neu.edu | |
Posted: November 5, 2012 | URL: http://www.math.neu.edu/bhmn/hurch12.html |