3 papers
math.AT2026
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…
math.AT2026
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…
math.AT2025
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.…