Topology Seminar: Jon Beardsley
Topic
Iterated Thom Spectra with Examples
Speakers
Details
Given a fiber sequence of n-fold loop spaces X-->Y-->Z, and morphism of n-fold loop spaces Y-->Pic(R) for R an E_{n+1}-ring spectrum, we describe a method of producing a new morphism of (n-1)-fold loop spaces Z-->Pic(MX), where MX is the Thom spectrum associated to the composition X-->Y-->Pic(R). This new morphism has associated Thom spectrum MY, but constructed directly as an MX-module. In particular this induces a relative Thom isomorphism for MY over MX: MY?_{MX} MY = MY?Z. We will see a rough description of this construction as well as many examples allowing us to find equivalent forms of relative smash products of spectra like MString, MSpin, HZ/2, X(n) and many others. We also describe a way to use this construction to identify certain obstructions to giving a complex orientation on an associative ring spectrum.
Additional Information
Location: PIMS Lounge, ESB 4133
Jon Beardsley, University of Washington
Jon Beardsley, University of Washington
This is a Past Event
Event Type
Scientific, Seminar
Date
November 9, 2016
Time
-
Location