On expansion and topological overlap

D. Dotterrer, T. Kaufman, U. Wagner, Geometriae Dedicata 195 (2018) 307–317.

Download
OA 412.49 KB

Journal Article | Published | English
Author
; ;
Department
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.
Publishing Year
Date Published
2018-08-01
Journal Title
Geometriae Dedicata
Volume
195
Issue
1
Page
307–317
IST-REx-ID

Cite this

Dotterrer D, Kaufman T, Wagner U. On expansion and topological overlap. Geometriae Dedicata. 2018;195(1):307–317. doi:10.1007/s10711-017-0291-4
Dotterrer, D., Kaufman, T., & Wagner, U. (2018). On expansion and topological overlap. Geometriae Dedicata, 195(1), 307–317. https://doi.org/10.1007/s10711-017-0291-4
Dotterrer, Dominic, Tali Kaufman, and Uli Wagner. “On Expansion and Topological Overlap.” Geometriae Dedicata 195, no. 1 (2018): 307–317. https://doi.org/10.1007/s10711-017-0291-4.
D. Dotterrer, T. Kaufman, and U. Wagner, “On expansion and topological overlap,” Geometriae Dedicata, vol. 195, no. 1, pp. 307–317, 2018.
Dotterrer D, Kaufman T, Wagner U. 2018. On expansion and topological overlap. Geometriae Dedicata. 195(1), 307–317.
Dotterrer, Dominic, et al. “On Expansion and Topological Overlap.” Geometriae Dedicata, vol. 195, no. 1, Springer, 2018, pp. 307–317, doi:10.1007/s10711-017-0291-4.
All files available under the following license(s):
Creative Commons License:
CC-BYCreative Commons Attribution 4.0 International Public License (CC-BY 4.0)
Main File(s)
File Name
Access Level
OA Open Access
Last Uploaded
2019-01-15T13:44:05Z


Material in IST:
Earlier Version

Export

Marked Publications

Open Data IST Research Explorer

Search this title in

Google Scholar