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Deformation Theory Seminar

Wednesday, May 23, 2007 - 2:00pm

John Carter

Franklin and Marshall

Location

University of Pennsylvania

DRL 4N30

The calculation of the homology of loop spaces for generalized homology theories such as Morava $K$-theory has been a long-standing problem. The Eilenberg-Moore spectral sequence could be a useful tool toward that end. One gap in the literature on this subject is useful general convergence criterion. I will discuss the construction of an Eilenberg-Moore type spectral sequence for Morava K-Theory, and some convergence criteria. In particular I have shown that the Eilenberg-Moore spectral sequence for Morava K-theory converges if the Eilenberg-Moore spectral sequence for ordinary homology collapses at E^2 and the homology satisfies certain finiteness conditions.