[Alta-Logic] Peripatetic seminar

[Robin Cockett]

When/where: Wed 9th March, 3:30pm, ICT616


Title:  Understanding Topological Homology theories for commutative rings

Who: Kristine Bauer

Abstract:

There is a very nice relationship between topological (co) homology theories and algebraic (co) homology theories.  Often, an algebraic theory (like Hochschild homology, Andre-Quillen homology or K-theory) has a topological analogue.  A good example is given by Andre-Quillen homology:  topologists understand this homology theory as a kind of linearization of a certain forgetful functor.  There's a catch, though --- the linearization relies on the fact that this particular forgetful functor preserves initial and terminal objects.  I will explain how to linearize functors from categories which don't have a terminal object.  Furthermore, I'll explain how to compute the linear approximations as well as higher degree approximations.  The computation is surprisingly discrete in nature, and relies on cosimplicial-simplicial sets.  In fact, all such approximations come from a functor of cosimplicial-simplicial sets which strives to approximate the empty set in a very systematic way!!

This talk is joint work with Rosona Eldred, Brenda Johnson and Randy McCarthy.  The results in this talk are applications of the results I spoke about in last week's math department colloquium, but no familliarity with my previous talk will be assumed!!