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A criterion for slope 1 homological stability

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arxiv 2407.01124 v1 pith:AW4EEMTI submitted 2024-07-01 math.KT

Mikala {O}rsnes Jansen , Jeremy Miller This is my paper · ORCID
classification math.KT
keywords mathbbhomologicalslopestabilityalgebrascriteriondiagonalenough
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abstract

We show that for nice enough $\mathbb{N}$-graded $\mathbb{E}_2$-algebras, a diagonal vanishing line in $\mathbb{E}_1$-homology of gives rise to slope $1$ homological stability. This is an integral version of a result by Kupers-Miller-Patzt.

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  1. A chromatic approach to homological stability

    math.AT 2025-08 accept novelty 8.0 of 10

    Under mild axioms on a graded E2-algebra over a positive-characteristic field, higher-order homological stability maps exist with slopes approaching 1, and the patterns are governed by a stability Hopf algebra.

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