[Binghamton Geometry Topology Seminar] This week: Yu Zhang

[sapir at math.binghamton.edu]

This week we will meet as usual on Thursday, November 21 at 2:50pm in
WH 100E.

Title: Topological Quillen localization of structured ring spectra

Abstract: Homotopy groups and stable homotopy groups of spaces are central
invariants in algebraic topology. Stable homotopy groups are comparatively
easier to work with, at the expense of losing certain information.
However, if we are working with nice spaces, nothing will be lost by
working stably: A map between nilpotent spaces induces homotopy groups
isomorphisms if and only if it induces stable homotopy groups
isomorphisms.

Structured ring spectra are spectra with certain algebraic structure
encoded by the action of an operad O. For such O-algebras, the analog of
stable homotopy groups are played by Topological Quillen (TQ) homology
groups. In this talk, we will draw the analogy between topological spaces
and O-algebras, discuss the TQ-localization of O-algebras, and show the
TQ-Whitehead theorem for homotopy pro-nilpotent O-algebras. Part of the
work in this talk is joint with John E. Harper.