A descriptive approach to higher derived limits

  • Nathaniel Bannister

    Carnegie Mellon University, Pittsburgh, USA
  • Jeffrey Bergfalk

    University of Barcelona, Barcelona, Spain
  • Justin Tatch Moore

    Cornell University, Ithaca, USA
  • Stevo Todorcevic

    University of Toronto, Toronto, ON, Canada
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Abstract

We present a new aspect of the study of higher derived limits. More precisely, we introduce a complexity measure for the elements of higher derived limits over the directed set of functions from to and prove that cocycles of this complexity are images of cochains of roughly the same complexity. In the course of this work, we isolate a partition principle for powers of directed sets and show that whenever this principle holds, the corresponding derived limit is additive; vanishing results for this limit are the typical corollary. The formulation of this partition hypothesis synthesizes and clarifies several recent advances in this area.

Cite this article

Nathaniel Bannister, Jeffrey Bergfalk, Justin Tatch Moore, Stevo Todorcevic, A descriptive approach to higher derived limits. J. Eur. Math. Soc. (2024), published online first

DOI 10.4171/JEMS/1464