Topology Seminar: Omar Antolin Camarena

  • Date: 10/28/2015
  • Time: 15:15
Lecturer(s):
Omar Antolin Camarena, UBC
Location: 

University of British Columbia

Topic: 

A simple universal property of Thom ring spectra

Description: 

A stable spherical fibration is classified by a map X → BGL₁(S) and Lewis showed that if this map is an infinite loop map or an n-fold loop map then the Thom spectrum is an E_∞- or E_n-ring spectrum, respectively. Ando, Blumberg, Hopkins, Gepner and Rezk introduced a new approach to Thom spectra using the language of ∞-categories. Using their approach, we will explain how to apply some simple (∞-)category theory to study multiplicative structures on Thom spectra, proving a generalization of Lewis's theorem and moreover characterizing the ring structure by a universal property. As an application I'll discuss a new (slightly simpler) proof of a remarkable theorem of Mahowald's realizing the Eilenberg-MacLane spectrum HF₂ as a Thom spectrum of a double loop map.

Other Information: 

Location: ESB 4133