Geodesic
Magnitude homology of graphs and discrete Morse theory on Asao–Izumihara complexes
Homology, homotopy, and applications, Tome 25 (2023) no. 1, pp. 331-343.

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

Recently, Asao and Izumihara introduced CW-complexes whose homology groups are isomorphic to direct summands of the graph magnitude homology group. In this paper, we study the homotopy type of the CW-complexes in connection with the diagonality of magnitude homology groups. We prove that the Asao–Izumihara complex is homotopy equivalent to a wedge of spheres for pawful graphs introduced by Y. Gu. The result can be considered as a homotopy type version of Gu’s result. We also formulate a slight generalization of the notion of pawful graphs and find new non-pawful diagonal graphs of diameter $2$.
DOI : 10.4310/HHA.2023.v25.n1.a17
Classification : 05C10, 05E45, 55N35
Keywords: magnitude homology, graph, discrete Morse theory 
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Yu Tajima; Masahiko Yoshinaga. Magnitude homology of graphs and discrete Morse theory on Asao–Izumihara complexes. Homology, homotopy, and applications, Tome 25 (2023) no. 1, pp. 331-343. doi : 10.4310/HHA.2023.v25.n1.a17. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2023.v25.n1.a17/

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