Algebraic & Geometric Topology Volume 26, issue 7 (2026)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Other MSP journals

Magnitude homology of geodesic spaces

Kiyonori Gomi

Algebraic & Geometric Topology 26 (2026) 2377–2419

DOI: 10.2140/agt.2026.26.2377

Bibliography

1	Y Asao, Magnitude homology of geodesic metric spaces with an upper curvature bound, Algebr. Geom. Topol. 21 (2021) 647 MR4250513
2	Y Asao, S O Ivanov, Magnitude homology is a derived functor, preprint (2024) arXiv:2402.14466
3	Y Asao, K Izumihara, Geometric approach to graph magnitude homology, Homology Homotopy Appl. 23 (2021) 297 MR4170472
4	M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
5	K Gomi, Smoothness filtration of the magnitude complex, Forum Math. 32 (2020) 625 MR4095498
6	Y Gu, Graph magnitude homology via algebraic Morse theory, preprint (2018) arXiv:1809.07240
7	R Hepworth, Magnitude cohomology, Math. Z. 301 (2022) 3617 MR4449723
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	T Leinster, The magnitude of metric spaces, Doc. Math. 18 (2013) 857 MR3084566
12	T Leinster, M Shulman, Magnitude homology of enriched categories and metric spaces, Algebr. Geom. Topol. 21 (2021) 2175 MR4334510
13	N Otter, Magnitude meets persistence: homology theories for filtered simplicial sets, Homology Homotopy Appl. 24 (2022) 365 MR4486246
14	A Papadopoulos, Metric spaces, convexity and non-positive curvature, 6, European Math. Soc. (2014) MR3156529
15	E H Spanier, Algebraic topology, Springer (1981) MR666554
16	Y Tajima, M Yoshinaga, Causal order complex and magnitude homotopy type of metric spaces, Int. Math. Res. Not. 2024 (2024) 3176 MR4707282
17	S Willerton, Torsion: graph magnitude homology meets combinatorial topology, The n-Category Café blog post (2018)