Date: Monday, March 14, 2022
Location: 1866 East Hall (3:00 PM to 4:00 PM)
Title: Operations on generalized TAQ (co)homology
Abstract: We review a bar spectral sequence that is amenable to understanding the mod p Topological Andre Quillen (co)homology of algebras over operads in the category of spectra. Then we focus on the examples of the commutative operad and the spectral Lie operad. Applying the method to the former yields all natural operations and relations on the homotopy groups of spectral partition Lie algebras and TAQ cohomology, thereby clarifying unpublished results of Kriz and BasterraMandell. On the other hand, mod p TAQ homology of certain spectral Lie algebras recovers the mod p homology of labelled configuration spaces by a result of Knudsen. We compute the E^2page of the associated bar spectral sequence, which is the Andre Quillen homology of spectral Lie algebras. While the bar spectral sequence almost never collapses, we conjecture a universal pattern of differentials.
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Speaker: Adela Zhang
Institution: MIT
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