Reconstructing $d$-manifold subcomplexes of cubes from their $(\lfloor d/2\rfloor +1)$-skeletons

Abstract

In 1984, Dancis proved that any $d$-dimensional simplicial manifold is determined by its $(\lfloor d/2\rfloor +1)$-skeleton. This paper adapts his proof to the setting of cubical complexes that can be embedded into a cube of arbitrary dimension. Under some additional conditions (for example, if the cubical manifold is a sphere), the result can be tightened to the $\lceil d/2\rceil$-skeleton when $d\ge 3$.

arXiv commentMinor corrections. To appear in Discrete & Computational Geometry. 12 pages, 1 figure