A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf
.
Filtered simplicial homology, graph dissimilarity and überhomology
[article]
2022
arXiv
pre-print
We introduce a filtration on the simplicial homology of a finite simplicial complex X using bi-colourings of its vertices. This yields two dual homology theories closely related to discrete Morse matchings on X. We give an explicit expression for the associated graded object of these homologies when X is the matching complex of the Tait graph of a plane graph G, in terms of subgraphs determined by certain matchings on the dual of G. We then use one of these homologies, in the case where X is a
arXiv:2105.03987v2
fatcat:dwuevieoafhwbgblcovl3xw7tq