5 papers
Manifold classification from the descriptive viewpoint
Jeffrey Bergfalk, Iian B. Smythe
We consider classification problems for manifolds and discrete subgroups of Lie groups from a descriptive set-theoretic point of view. This work is largely foundational in concepti…
Whitehead's problem and condensed mathematics
Jeffrey Bergfalk, Chris Lambie-Hanson, Jan Å aroch
One of the better-known independence results in general mathematics is Shelah's solution to Whitehead's problem of whether implies that an abelian…
Infinitary combinatorics in condensed math and strong homology
Jeffrey Bergfalk, Chris Lambie-Hanson
Recent advances in our understanding of higher derived limits carry multiple implications in the fields of condensed and pyknotic mathematics, as well as for the study of strong ho…
Higher limits of wider systems
Jeffrey Bergfalk, Matteo Casarosa
Write for what might be described as the most elementary nontrivial inverse system of abelian groups indexed by the functions from the cardinal to the set of n…
An introduction to higher walks
Jeffrey Bergfalk
The following is an introduction to the study of higher walks, by which we mean a family of higher-dimensional extensions of Todorcevic's method of walks on the ordinals. After a b…