Topology at IU

Loading

Wednesday April 22 at 4:00 PM in RH 104: Itamar Mor (UIUC), “The synthetic EHP sequence”; The lower central series is a classical tool that deforms any group into an abelian group (in fact, into a Lie algebra). In the 60s, Curtis and Rector used this to define a version of the unstable Adams spectral sequence, computing the homotopy groups of a space from the free (derived) Lie algebra on its homology. I'll describe a categorification of this construction in the spirit of synthetic spectra, which gives a way to deform a space into a derived Lie algebra. Many classical constructions in unstable homotopy theory may be deformed in this way: for example, I will discuss how this may be used to relate the classical EHP spectral sequence (which I will introduce) to Curtis' algebraic EHP spectral sequence, which can essentially be computed by machine.