Scalable spaces
成果类型：
Article
署名作者：
Berdnikov, Aleksandr; Manin, Fedor
署名单位：
Institute for Advanced Study - USA; University of California System; University of California Santa Barbara
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/s00222-022-01118-9
发表日期：
2022
页码：
1055-1100
关键词：
摘要：
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.