Discrete Morse Theory for Weighted Simplicial Complexes
arXiv:1901.01716 · doi:10.1016/j.topol.2019.107038
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.
arXiv comment19 pages, to appear in Topology and its Applications
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- Discrete Differential Calculus on Simplicial Complexes and Constrained Homology