---
res:
bibo_abstract:
- 'We give a detailed and easily accessible proof of Gromovâ€™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.@eng'
bibo_authorlist:
- foaf_Person:
foaf_givenName: Dominic
foaf_name: Dotterrer, Dominic
foaf_surname: Dotterrer
- foaf_Person:
foaf_givenName: Tali
foaf_name: Kaufman, Tali
foaf_surname: Kaufman
- foaf_Person:
foaf_givenName: Uli
foaf_name: Wagner, Uli
foaf_surname: Wagner
foaf_workInfoHomepage: http://www.librecat.org/personId=36690CA2-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0002-1494-0568
bibo_doi: 10.1007/s10711-017-0291-4
bibo_issue: '1'
bibo_volume: 195
dct_date: 2018^xs_gYear
dct_language: eng
dct_publisher: Springer@
dct_title: On expansion and topological overlap@
...