Scalable spaces
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222_2022_1118_ReferencePDF.pdf
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828.29 KB
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Author(s)
Berdnikov, Aleksandr
Manin, Fedor
Date Issued
May 9, 2022
Publisher
Springer Berlin Heidelberg
Citation
Berdnikov, Aleksandr and Manin, Fedor. 2022. "Scalable spaces."
Version
Author's final manuscript
Abstract
Abstract
Scalable spaces are simply connected compact manifolds or finite complexes whose real cohomology algebra embeds in their algebra of (flat) differential forms. This is a rational homotopy invariant property and all scalable spaces are formal; indeed, scalability can be thought of as a metric version of formality. They are also characterized by particularly nice behavior from the point of view of quantitative homotopy theory. Among other results, we show that spaces which are formal but not scalable provide counterexamples to Gromov’s long-standing conjecture on distortion in higher homotopy groups.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00222-022-01118-9
