@article{742,
abstract = {We give a detailed and easily accessible proof of Gromov’s Topological Overlap Theorem. Let X be a finite simplicial complex or, more generally, a finite polyhedral cell complex of dimension d. Informally, the theorem states that if X has sufficiently strong higher-dimensional expansion properties (which generalize edge expansion of graphs and are defined in terms of cellular cochains of X) then X has the following topological overlap property: for every continuous map (Formula presented.) there exists a point (Formula presented.) that is contained in the images of a positive fraction (Formula presented.) of the d-cells of X. More generally, the conclusion holds if (Formula presented.) is replaced by any d-dimensional piecewise-linear manifold M, with a constant (Formula presented.) that depends only on d and on the expansion properties of X, but not on M.},
author = {Dotterrer, Dominic and Kaufman, Tali and Wagner, Uli},
journal = {Geometriae Dedicata},
number = {1},
pages = {307–317},
publisher = {Springer},
title = {{On expansion and topological overlap}},
doi = {10.1007/s10711-017-0291-4},
volume = {195},
year = {2018},
}