A criterion for slope 1 homological stability

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.

arXiv comment7 pages. Comments welcome