6 papers · 1 filter
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…
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…
The definable content of homological invariants I: &
Jeffrey Bergfalk, Martino Lupini, Aristotelis Panagiotopoulos
This is the first installment in a series of papers in which we illustrate how classical invariants of homological algebra and algebraic topology can be enriched with additional de…
The definable content of homological invariants II: Äech cohomology and homotopy classification
Jeffrey Bergfalk, Martino Lupini, Aristotelis Panagiotopoulos
This is the second installment in a series of papers applying descriptive set theoretic techniques to both analyze and enrich classical functors from homological algebra and algebr…