Algebraic filling inequalities and cohomological width

摘要

In his work on singularities, expanders and topology of maps, Gromov showed, using isoperimetric inequalities in graded algebras, that every real-valued map on the n-torus admits a fibre whose homological size is bounded below by some universal constant depending on n. He obtained similar estimates for maps with values in finite-dimensional complexes, by a Lusternik-Schnirelmann-type argument.