Speaker: Shahzad Kalloo (Wayne State University)

Title: A Novel Eilenberg-Moore Spectral Sequence for Continuous Group Cohomology

Abstract: 

In the 70's Jack Morava observed a wondrous connection between continuous group cohomology and the E2-pages of certain generalized Adams Spectral Sequences following work of Tate.

In this talk we construct and study an Eilenberg-Moore spectral sequence that calculates the homotopy groups of certain Galois covers of the K(2)-local sphere via continuous group cohomology. These Galois covers of the K(2)-local sphere are constructed as the homotopy fixed-points of certain subgroups--namely, Lazard's 'equi-p-valued groups'--of the Morava stabilizer group acting on Morava E-theory. These subgroups are of interest as Lazard's Isomorphism Theorem establishes that the cohomology of an equi-p-valued group with trivial coefficients is an exterior algebra.

We shall first recall a few basic facts about the Morava Stabilizer groups and discuss some of their relevant features, one of which is that they are p-adic analytic lie groups. We then construct our Eilenberg Moore Spectral sequence and examine convergence. Finally we use our EMSS to calculate the cohomology of equi-p-valued groups with trivial coefficients and with nontrivial coefficients to study generalizations of the Lazard isomorphism.

Location: Nelson Library (1146 Faculty/Administration Building)

Time: 2:00 - 3:00 PM