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2021 Magnitude homology of geodesic metric spaces with an upper curvature bound
Yasuhiko Asao
Algebr. Geom. Topol. 21(2): 647-664 (2021). DOI: 10.2140/agt.2021.21.647

Abstract

We study the magnitude homology of geodesic metric spaces of curvature κ, especially CAT(κ) spaces. We will show that the magnitude homology MHnl(X) of such a metric space X vanishes for small l and all n>0. Consequently, we can compute magnitude homology in small length gradings for spheres 𝕊n, the Euclidean spaces 𝔼n, the hyperbolic spaces n and real projective spaces n with the standard metric. We also show that the existence of a closed geodesic in a metric space guarantees the nontriviality of magnitude homology.

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Yasuhiko Asao. "Magnitude homology of geodesic metric spaces with an upper curvature bound." Algebr. Geom. Topol. 21 (2) 647 - 664, 2021. https://doi.org/10.2140/agt.2021.21.647

Information

Received: 19 May 2019; Revised: 7 April 2020; Accepted: 19 June 2020; Published: 2021
First available in Project Euclid: 28 May 2021

Digital Object Identifier: 10.2140/agt.2021.21.647

Subjects:
Primary: 51F99, 55N35

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.21 • No. 2 • 2021
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