{"date_published":"2018-08-01T00:00:00Z","publication_status":"published","issue":"1","department":[{"_id":"UlWa"}],"abstract":[{"text":"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.","lang":"eng"}],"file":[{"file_size":412486,"date_created":"2019-01-15T13:44:05Z","file_id":"5835","date_updated":"2020-07-14T12:47:58Z","file_name":"s10711-017-0291-4.pdf","creator":"kschuh","access_level":"open_access","content_type":"application/pdf","relation":"main_file","checksum":"d2f70fc132156504aa4c626aa378a7ab"}],"type":"journal_article","day":"01","article_processing_charge":"Yes (via OA deal)","month":"08","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_updated":"2023-09-27T12:29:57Z","title":"On expansion and topological overlap","quality_controlled":"1","related_material":{"record":[{"status":"public","id":"1378","relation":"earlier_version"}]},"status":"public","oa":1,"oa_version":"Published Version","date_created":"2018-12-11T11:48:16Z","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publisher":"Springer","scopus_import":"1","citation":{"ieee":"D. Dotterrer, T. Kaufman, and U. Wagner, “On expansion and topological overlap,” <i>Geometriae Dedicata</i>, vol. 195, no. 1. Springer, pp. 307–317, 2018.","mla":"Dotterrer, Dominic, et al. “On Expansion and Topological Overlap.” <i>Geometriae Dedicata</i>, vol. 195, no. 1, Springer, 2018, pp. 307–317, doi:<a href=\"https://doi.org/10.1007/s10711-017-0291-4\">10.1007/s10711-017-0291-4</a>.","short":"D. Dotterrer, T. Kaufman, U. Wagner, Geometriae Dedicata 195 (2018) 307–317.","ista":"Dotterrer D, Kaufman T, Wagner U. 2018. On expansion and topological overlap. Geometriae Dedicata. 195(1), 307–317.","apa":"Dotterrer, D., Kaufman, T., &#38; Wagner, U. (2018). On expansion and topological overlap. <i>Geometriae Dedicata</i>. Springer. <a href=\"https://doi.org/10.1007/s10711-017-0291-4\">https://doi.org/10.1007/s10711-017-0291-4</a>","chicago":"Dotterrer, Dominic, Tali Kaufman, and Uli Wagner. “On Expansion and Topological Overlap.” <i>Geometriae Dedicata</i>. Springer, 2018. <a href=\"https://doi.org/10.1007/s10711-017-0291-4\">https://doi.org/10.1007/s10711-017-0291-4</a>.","ama":"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>"},"language":[{"iso":"eng"}],"pubrep_id":"912","_id":"742","page":"307–317","doi":"10.1007/s10711-017-0291-4","author":[{"last_name":"Dotterrer","first_name":"Dominic","full_name":"Dotterrer, Dominic"},{"first_name":"Tali","last_name":"Kaufman","full_name":"Kaufman, Tali"},{"first_name":"Uli","last_name":"Wagner","full_name":"Wagner, Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568"}],"has_accepted_license":"1","publication":"Geometriae Dedicata","external_id":{"isi":["000437122700017"]},"isi":1,"file_date_updated":"2020-07-14T12:47:58Z","ddc":["514","516"],"project":[{"grant_number":"PP00P2_138948","_id":"25FA3206-B435-11E9-9278-68D0E5697425","name":"Embeddings in Higher Dimensions: Algorithms and Combinatorics"}],"intvolume":"       195","volume":195,"publist_id":"6925","year":"2018"}