On expansion and topological overlap
Dotterrer, Dominic
Kaufman, Tali
Wagner, Uli
ddc:514
ddc:516
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.
Springer
2018
info:eu-repo/semantics/article
doc-type:article
text
http://purl.org/coar/resource_type/c_6501
https://research-explorer.app.ist.ac.at/record/742
https://research-explorer.app.ist.ac.at/download/742/5835
Dotterrer D, Kaufman T, Wagner U. On expansion and topological overlap. <i>Geometriae Dedicata</i>. 2018;195(1):307–317. doi:<a href="https://doi.org/10.1007/s10711-017-0291-4">10.1007/s10711-017-0291-4</a>
eng
info:eu-repo/semantics/altIdentifier/doi/10.1007/s10711-017-0291-4
info:eu-repo/grantAgreement/FWF//PP00P2_138948
info:eu-repo/semantics/openAccess