A descriptive approach to higher derived limits

A descriptive approach to higher derived limits

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 \Omega of functions from \mathbb{N} to \mathbb{N} and prove that cocycles of this complexity are images of cochains of roug...

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Veröffentlicht in:Journal of the European Mathematical Society : JEMS 2024-06
Hauptverfasser: Bannister, Nathaniel, Bergfalk, Jeffrey, Moore, Justin Tatch, Todorcevic, Stevo
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container_title Journal of the European Mathematical Society : JEMS
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creator Bannister, Nathaniel
Bergfalk, Jeffrey
Moore, Justin Tatch
Todorcevic, Stevo
description 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 \Omega of functions from \mathbb{N} to \mathbb{N} 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 \lim\nolimits^{n} 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.
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title A descriptive approach to higher derived limits
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