Spectral sequences via presheaves

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• Sarah Whitehouse (University of Sheffield)
• Monday 03 June 2024, 15:30-16:30
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TRH - Topology, representation theory and higher structures

The talk will cover homotopy theory associated with the category of spectral sequences. For each r, maps which are quasi-isomorphisms on the r page provide a class of weak equivalences. We introduce the category of extended spectral sequences and show that this is bicomplete by analysis of a certain presheaf category modelled on discs. We endow the category of extended spectral sequences with various model category structures. One of these has the property that spectral sequences is a homotopically full subcategory and so, by results of Meier, this exhibits the category of spectral sequences as a fibrant object in the Barwick-Kan  model structure on relative categories. We also note how the presheaf approach provides some insight into the décalage functor on spectral  sequences. This is joint work with Muriel Livernet.

This talk is part of the Isaac Newton Institute Seminar Series series.

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