Stronger expansion for polynomial-degree abelian Cayley complexes

Determine whether polynomial-degree abelian Cayley complexes can satisfy the stronger assumptions used in low-soundness agreement testing, including coboundary expansion or cosystolic expansion of associated faces complexes.

Background

The constructions in the paper establish local spectral expansion but do not establish cofilling constants or cosystolic expansion. The paper emphasizes that applications such as low-soundness agreement testing may require stronger expansion properties than the local spectral bounds proved here.

The unresolved question is whether abelian Cayley complexes whose degree is polynomial in the ambient dimension can also meet these stronger coboundary or cosystolic expansion requirements for associated face complexes.