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A Simplicial Complex is Uniquely Determined by Its Set of Discrete Morse Functions

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Abstract

We prove that a connected simplicial complex is uniquely determined by its complex of discrete Morse functions. This settles a question raised by Chari and Joswig. In the 1-dimensional case, this implies that the complex of rooted forests of a connected graph G completely determines G.

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Acknowledgements

Researchers of CONICET. Partially supported by grants ANPCyT PICT-2011-0812, CONICET PIP 112-201101-00746 and UBACyT 20020130100369.

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Authors and Affiliations

  1. Departamento de Matemática-IMAS, FCEyN, Universidad de Buenos Aires, C1428EGA, Buenos Aires, Argentina

    Nicolas Ariel Capitelli & Elias Gabriel Minian

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  1. Nicolas Ariel Capitelli
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  2. Elias Gabriel Minian
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Correspondence to Elias Gabriel Minian.

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Capitelli, N.A., Minian, E.G. A Simplicial Complex is Uniquely Determined by Its Set of Discrete Morse Functions. Discrete Comput Geom 58, 144–157 (2017). https://doi.org/10.1007/s00454-017-9865-z

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  • DOI: https://doi.org/10.1007/s00454-017-9865-z

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