4 papers
Homotopy theories via the magnitude-path spectral sequence
Muriel Livernet, Emily Roff, Sarah Whitehouse
We introduce a family of homotopy theories for generalized metric spaces with natural number distances, via the magnitude-path spectral sequence (MPSS). The first page of the MPSS…
Spectral sequences via linear presheaves
Muriel Livernet, Sarah Whitehouse
We study homotopy theory of the category of spectral sequences with respect to the class of weak equivalences given by maps which are quasi-isomorphisms on a fixed page. We introdu…
Model category structures on truncated multicomplexes for complex geometry
Joana Cirici, Muriel Livernet, Sarah Whitehouse
To a bicomplex one can associate two natural filtrations, the column and row filtrations, and then two associated spectral sequences. This can be generalized to -multicomplexes.…
Steenrod operations on polyhedral products
Sanjana Agarwal, Jelena GrbiÄ, Michele Intermont +3
We describe the action of the mod Steenrod algebra on the cohomology of various polyhedral products and related spaces. We carry this out for Davis-Januszkiewicz spaces and the…