Pairings in a Ring Spectrum-Based Bousfield-Kan Spectral Sequence

Author

Jonathan Toledo, The Graduate Center, City University of New YorkFollow

Date of Degree

6-2023

Document Type

Dissertation

Degree Name

Ph.D.

Program

Mathematics

Advisor

Robert Thompson

Committee Members

Martin Bendersky

Mahmoud Zeinalian

Subject Categories

Algebra | Geometry and Topology

Abstract

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.

Recommended Citation

Toledo, Jonathan, "Pairings in a Ring Spectrum-Based Bousfield-Kan Spectral Sequence" (2023). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/5331