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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A chromatic approach to homological stability
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.