Algebra/Topology seminar

Dustin Clausen, An example of the use of infinity-categorification.  

This will be a continuation of my previous talk on reciprocity laws via homotopy theory, but it won't be necessary to know anything from that talk to understand this one.  We will give an introduction to homotopy sheaves on topological spaces, as well as one or two interesting full subcategories of these.  Then we'll see how to use these categories to prove the following fact: for a pointed compact orientable smooth manifold (M,m), the suspension spectrum of the one point compactification of the tangent space T_m(M) can be canonically described in terms of the "spherical cochains" on M.  All of this stuff relies on ideas and constructions due to Jacob Lurie.