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Reconstructing d-Manifold Subcomplexes of Cubes from Their \((\lfloor d/2 \rfloor + 1)\)-Skeletons

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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 \(d\ge 3\).

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Acknowledgements

This research was partially supported by a graduate fellowship from NSF grant DMS-1664865. We thank Steven Klee, Margaret Bayer, Raman Sanyal, the anonymous reviewers, and especially Isabella Novik for many helpful suggestions.

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  1. University of Washington, Seattle, USA

    Rowan Rowlands

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  1. Rowan Rowlands
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Correspondence to Rowan Rowlands.

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Rowlands, R. Reconstructing d-Manifold Subcomplexes of Cubes from Their \((\lfloor d/2 \rfloor + 1)\)-Skeletons. Discrete Comput Geom 67, 492–502 (2022). https://doi.org/10.1007/s00454-021-00321-4

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  • DOI: https://doi.org/10.1007/s00454-021-00321-4

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