Algebraic K-Theory Seminar
Gijs Heuts
Universiteit Utrecht
Lie algebras and v_n-periodic spaces
Abstract: I will discuss a homotopy theory obtained from that of pointed spaces by inverting the maps inducing isomorphisms in v_n-periodic homotopy groups. The case n = 0 corresponds to rational homotopy theory. In analogy with Quillen’s results in the rational case, I will outline how this v_n-periodic homotopy theory is equivalent to the homotopy theory of Lie algebras in the category of T(n)-local spectra. One can also compare it to the homotopy theory of cocommutative coalgebras in the category of T(n)-local spectra. For n > 0 these theories are no longer equivalent; the failure can be expressed in terms of the convergence of the Goodwillie tower of the identity in periodic homotopy.
Monday April 23, 2018 at 1:00 PM in SEO 1227