Publications

Unpublished

2026

1. Periodic families in the homology of GL_n(F_2)

   Kelly Wang

   2026

   abstract arXiv pdf

   We construct infinite families of nonzero classes in H_d(GL_n(\F_2);\F_2) along lines of the form d =\frac23n + (constant), thereby showing that the known slope \frac23-stability for these homology groups are optimal. Using the new stability Hopf algebra perspective of Randal-Williams, our computations in addition recover the slope-\frac23 stability for \GL_n(\Z) with coefficients in \F_2, improve that for \Aut(F_n) to \frac23, and demonstrate that those slopes are optimal. Perhaps of independent interest, we also provide a manual for computing stability Hopf algebras over F_2.

   @unpublished{periodic_families,
     title = {Periodic families in the homology of $GL_n(F_2)$},
     author = {Wang, Kelly},
     year = {2026},
   }