图的幅度同调与 Asao-Izumihara 复形上的离散 Morse 理论
Magnitude homology of graphs and discrete Morse theory on Asao-Izumihara complexes
AI总结：
本文研究 Asao-Izumihara 复形的同伦型与图幅度同调可对角化性的关系，证明 pawful 图的该复形同伦等价于球面的一点并，并推广 pawful 图概念，找到新的直径为 2 的非 pawful 可对角化图。
摘要：
最近，Asao 和 Izumihara 引入了 CW 复形，其同调群同构于图幅度同调群的直和项。本文研究这些 CW 复形的同伦型与幅度同调群可对角化性之间的联系。我们证明，对于 Y. Gu 引入的 pawful 图，Asao-Izumihara 复形同伦等价于球面的一点并。该结果可视为 Gu 结果的同伦型版本。我们还对 pawful 图的概念提出了一个轻微推广，并找到了新的直径为 $2$ 的非 pawful 可对角化图。
英文摘要：
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 $2$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
