Scalable spaces

Scalable spaces are simply connected compact manifolds or finite complexes whose real cohomology algebra embeds in their of (flat) differential forms. This is a rational homotopy invariant property and all scalable formal; indeed, scalability can be thought as metric version formality. They also characterized by particularly nice behavior from the point view quantitative theory. Among other results, we show that which formal but not provide counterexamples to Gromov’s long-standing conjecture on distortion higher groups.