Geodesic
Geometric approach to graph magnitude homology
Homology, homotopy, and applications, Tome 23 (2021) no. 1, pp. 297-310.

Voir la notice de l'article provenant de la source International Press of Boston

In this paper, we introduce a new method to compute the magnitude homology of general graphs. To each direct sum component of the magnitude chain complexes, we assign a pair of simplicial complexes whose simplicial chain complex is isomorphic to it. First we state our main theorem specialized to trees, which gives another proof for the known fact that trees are diagonal. After that, we consider general graphs, which may have cycles. We also demonstrate some computation as an application.
DOI : 10.4310/HHA.2021.v23.n1.a16
Classification : 55U05
Keywords: magnitude homology, simplicial homology 
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Yasuhiko Asao; Kengo Izumihara. Geometric approach to graph magnitude homology. Homology, homotopy, and applications, Tome 23 (2021) no. 1, pp. 297-310. doi : 10.4310/HHA.2021.v23.n1.a16. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2021.v23.n1.a16/

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