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The mod 2 homology of infinite loopspaces

Le : 27/05/2013 15h30
Par : Nick Kuhn, University of Virginia
Lieu : I 001
Lien web :
Résumé : A spectrum X is a sequence of spaces, X_0, X_1, ..., with each space homotopy equivalent to the loop space of the next on the list. The homology of X is then the colimit of the homology of these spaces. We discuss how to try to recover the mod 2 homology of X_0, a highly structured object, from the mod 2 homology of X, viewed as a right module over the Steenrod algebra. Our method is to use a spectral sequence coming from a Goodwillie tower. In good cases, the end of the spectral sequence is determined by derived functors of destabilization applied to the homology of X. This is joint work with Jason McCarty.