Year: 2026
Type: preprint
Abstract: Two recent constructions independently give bigraded commutative Hopf algebra structures on the homology of $\mathrm{GL}(\mathbb{Z})$ with rational Steinberg coefficients. One, by Ash--Miller--Patzt, uses the sharbly resolution. The other, by Brown--Chan--Galatius--Payne, uses the Quillen spectral sequence and rank-filtered maps on $BK(\mathbb{Z})$. We prove that the two structures coincide. Both are induced by join and parabolic restriction operations on Steinberg modules.
Source: arXiv (Cornell University)
Authors: Pal, Urshita, Payne, Sam
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7215035387