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Magnitude homology equivalence of Euclidean sets

Adrián Doña Mateo and Tom Leinster

Algebraic & Geometric Topology 26 (2026) 599–624
Bibliography
1 Y Asao, Magnitude homology of geodesic metric spaces with an upper curvature bound, Algebr. Geom. Topol. 21 (2021) 647 MR4250513
2 J A Barceló, A Carbery, On the magnitudes of compact sets in Euclidean spaces, Amer. J. Math. 140 (2018) 449 MR3783215
3 L Caputi, C Collari, On finite generation in magnitude (co)homology and its torsion, Bull. Lond. Math. Soc. 56 (2024) 3434 MR4828025
4 S Cho, Quantales, persistence, and magnitude homology, preprint (2019) arXiv:1910.02905
5 H Gimperlein, M Goffeng, On the magnitude function of domains in Euclidean space, Amer. J. Math. 143 (2021) 939 MR4270261
6 C Giusti, G Menara, Eulerian magnitude homology: subgraph structure and random graphs, preprint (2024) arXiv:2403.09248
7 K Gomi, Magnitude homology of geodesic space, preprint (2019) arXiv:1902.07044
8 R Hepworth, S Willerton, Categorifying the magnitude of a graph, Homology Homotopy Appl. 19 (2017) 31 MR3683605
9 B Jubin, On the magnitude homology of metric spaces, preprint (2018) arXiv:1803.05062
10 R Kaneta, M Yoshinaga, Magnitude homology of metric spaces and order complexes, Bull. Lond. Math. Soc. 53 (2021) 893 MR4275098
11 F W Lawvere, Metric spaces, generalized logic, and closed categories, Rend. Sem. Mat. Fis. Milano 43 (1973) 135 MR352214
12 T Leinster, The magnitude of metric spaces, Doc. Math. 18 (2013) 857 MR3084566
13 T Leinster, M W Meckes, The magnitude of a metric space : from category theory to geometric measure theory, from: "Measure theory in non-smooth spaces" (editor N Gigli), de Gruyter (2017) 156 MR3701739
14 T. Leinster, M. Meckes, Magnitude : a bibliography, (2024)
15 T Leinster, M Shulman, Magnitude homology of enriched categories and metric spaces, Algebr. Geom. Topol. 21 (2021) 2175 MR4334510
16 M W Meckes, Magnitude, diversity, capacities, and dimensions of metric spaces, Potential Anal. 42 (2015) 549 MR3306695
17 N Otter, Magnitude meets persistence : homology theories for filtered simplicial sets, Homology Homotopy Appl. 24 (2022) 365 MR4486246
18 A Papadopoulos, Metric spaces, convexity and nonpositive curvature, 6, European Mathematical Society (2005) MR2132506
19 E. Roff, The size and shape of things: magnitude, diversity, homology, PhD thesis, University of Edinburgh (2022)
20 R Sazdanovic, V Summers, Torsion in the magnitude homology of graphs, J. Homotopy Relat. Struct. 16 (2021) 275 MR4266207
21 R Schneider, Convex bodies : the Brunn–Minkowski theory, 151, Cambridge Univ. Press (2014) MR3155183
22 Y Tajima, M Yoshinaga, Causal order complex and magnitude homotopy type of metric spaces, Int. Math. Res. Not. 2024 (2024) 3176 MR4707282
23 J H Wells, L R Williams, Embeddings and extensions in analysis, 84, Springer (1975) MR461107