Existence of bounded-degree F2 coboundary expanders in every dimension

Theorem 1.1: for every $d\ge3$ there are $D$, $\varepsilon>0$ and finite connected pure $d$-dimensional complexes $X_m$ with $|X_m(0)|\to\infty$, every vertex in at most $D$ top faces, and $\|\delta_if\|\ge\varepsilon\,\mathrm{dist}(f,B^i)$ for all $i<d$. The complexes are $d$-skeleta of congruence quotients modulo $t^m$ of a coset complex for the Iwahori-type subgroup of $\mathrm{SL}_{2d+1}(k[t])$ over a large odd prime field; cohomology vanishing comes from an affine twin building, and quantitative expansion from Oppenheim-Valentiner-Branth. Constants depend on $d$ and are not explicit; only $\mathbb{F}_2$ coefficients are treated.

Theorem 1.1: for every $d\ge3$ there are $D$, $\varepsilon>0$ and finite connected pure $d$-dimensional complexes $X_m$ with $|X_m(0)|\to\infty$, every vertex in at most $D$ top faces, and $\|\delta_if\|\ge\varepsilon\,\mathrm{dist}(f,B^i)$ for all $i<d$. The complexes are $d$-skeleta of congruence quotients modulo $t^m$ of a coset complex for the Iwahori-type subgroup of $\mathrm{SL}_{2d+1}(k[t])$ over a large odd prime field; cohomology vanishing comes from an affine twin building, and quantitative expansion from Oppenheim-Valentiner-Branth. Constants depend on $d$ and are not explicit; only $\mathbb{F}_2$ coefficients are treated.