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Discrete Morse Theory for Weighted Simplicial Complexes
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.Comment: 19 pages, to appear in Topology and its Application