Date of Degree
Algebra | Geometry and Topology
Bousfield and Kan traditionally formulated their homotopy spectral sequence over a simplicial set X resolved with respect to a ring R. By considering an adequate category of ring spectra, one can take a ring spectrum E, create from it a functor of a triple on the category of simplicial sets, and build a cosimplicial simplicial set EX. The homotopy spectral sequence can then be formed over such cosimplicial spaces by a similar construction to the original. Pairings can be established on these spectral sequences, and, for nice enough spaces, these pairings on the E2-terms coincide with certain pairings on Ext groups.
Toledo, Jonathan, "Pairings in a Ring Spectrum-Based Bousfield-Kan Spectral Sequence" (2023). CUNY Academic Works.