Online seminar, U. Haifa Topology & Geometry seminar on March 21, 2021
A recording of the talk is available here.
Topology & Geometry Seminar
Speaker: Agnès Beaudry, University of Colorado Boulder
Topic: The Picard group of higher real K-theories from an equivariant perspective
Place: This is an online seminar. Please email David Blanc “blanc at math dot haifa dot ac dot il” for the Zoom ID and password.
Date: Sunday, March 21, 2021
Real K-theory, KO can be realized as the fixed point of K-theory by the action of a group of order 2 arising from complex conjugation. Interestingly, the Picard group of KO, that is, the collection of invertible KO-module spectra is a cyclic group of order 8, the periodicity of KO. Central objects of study in chromatic and equivariant homotopy theory are the “higher K-theories” or Lubin-Tate spectra. They come equipped with actions of finite groups, giving rise to periodic spectra commonly known as the “higher real K-theories”. An open problem is to understand the Picard groups of these higher real K-theories. When is it cyclic? What is its structure? Equivariant techniques give insight on this problem. I will present this perspective and some results about these Picard groups in this talk.