Iterated Quotients of Ring Spectra and Hopf-Galois Extensions

Geometry Topology Seminar
Monday, April 11, 2016 - 2:00pm
1 hour (actually 50 minutes)
Skiles 006
Johns Hopkins University
Given an action by a loop space on a structured ring spectrum we describe how to produce its associated quotient ring spectrum.  We then describe how this structure may be leveraged to produce intermediate Hopf-Galois extensions of ring spectra, analogous to the way one produces intermediate Galois extensions from normal subgroups of a Galois group. We will give many examples of this structure in classical cobordism spectra and in particular describe an entirely new construction of the complex cobordism spectrum which bears a striking resemblance to Lazard's original construction of the Lazard ring by iterated extensions.