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arXiv · 1901.01716

Discrete Morse Theory for Weighted Simplicial Complexes

Chengyuan Wu·Shiquan Ren·Jie Wu·Kelin Xia
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Abstract

In this paper, we study Forman's discrete Morse theory in the context of weighted homology. We develop weighted versions of classical theorems in discrete Morse theory. A key difference in the weighted case is that simplicial collapses do not necessarily preserve weighted homology. We work out some sufficient conditions for collapses to preserve weighted homology, as well as study the effect of elementary removals on weighted homology. An application to sequence analysis is included, where we study the weighted ordered complexes of sequences.

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Chengyuan Wu, Shiquan Ren, Jie Wu, Kelin Xia. 2019-01-07. Discrete Morse Theory for Weighted Simplicial Complexes. https://doi.org/10.1016/j.topol.2019.107038

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