EVENT DETAILS AND ABSTRACT

Title: A Segal conjecture for p-completed classifying spaces
Speaker: Professor Kari Ragnarsson
Speaker Info: Northwestern University
Brief Description:
Special Note:
Abstract:

As was predicted by Adams and Miller, and shown by Lewis-May-McClure, one consequence of Carlsson's solution of the Segal conjecture is the description of the group {BG,BH} of homotopy classes of stable maps between classifying spaces of finite groups G and H as the completion of A(G,H) at the augmentation ideal I(G) of the Burnside ring A(G). (Here A(G,H) denotes the Grothendieck group completion of the monoid of isomorphism classes of finite (G x H)-sets such that the induced H-action is free, and A(G) can be regarded as the special case where H is the trivial group.) Unfortunately such completions are very difficult to calculate in general. However, Lewis-May showed that in the special case where G is a p-group, I(G)-adic completion agrees with p-adic completion