OpenAI reports bounded-degree coboundary expanders in higher dimensions

For every integer d≥3, there are arbitrarily large finite pure connected d-dimensional simplicial complexes with uniformly bounded vertex degree and uniform F₂ coboundary expansion in every degree below d.

Curated contributions 1

Understand the problem ↓

Understanding the problem

Read the background

For every integer d≥3, there are arbitrarily large finite pure connected d-dimensional simplicial complexes with uniformly bounded vertex degree and uniform F₂ coboundary expansion in every degree below d.

Why it matters

If correct, supplies the missing higher-dimensional bounded-vertex-degree coboundary expanders.

What counts as progress

Do bounded-vertex-degree F₂ coboundary expanders exist in every higher dimension?

Website timeline

Publication dates and editorial changes.