Finite non-positively curved complex model conjecture for compact two-dimensional spaces

Let $X$ be a compact, two-dimensional, non-positively curved space. Finite complex model conjecture. The space $X$ is homotopy equivalent to a finite, two-dimensional, non-positively curved Euclidean complex. Such a description would give a finite combinatorial model for compact two-dimensional non-positively curved spaces and may be relevant to geometric group theory; the paper presents this as an unresolved conjecture.