Topology: Jason McCarty, University of Virginia

“A Spectral Sequence for the Homology of Ω∞ X"

Tuesday, May 29, 2012
  11:10 a.m.–Noon

Location: Surge Building 268
  Parking Information

Category: Seminar

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Description: I will discuss joint work with N. Kuhn about a Goodwillie tower spectral sequence converging to H*( Ω∞ X), the mod 2 homology of the zeroth space of a connected spectrum X. Dyer-Lashof operations on the spectral sequence lead to "universal" differentials that hold for all spectra. These then lead to an algebraic version of the spectral sequence, whose pages can be completely described in terms of the derived functors of "destabilization" studied by W. Singer and others. The two spectral sequences coincide until the first non-universal, or "rogue," differential. Using this identification, the spectral sequence for various spectra can be completely understood, including all Eilenberg-MacLane spectra. I will finish by discussing some examples of non-connected spectra where the spectral sequence unexpectedly converges to the right answer, or nearly so.

Additional Information: Topology Seminar site

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Open to: General Public
Admission: Free
Sponsor: Mathematics

Contact Information:
Dr. Julie Bergner

jbergner@math.ucr.edu