{"file":[{"file_name":"IST-2016-623-v1+1_LIPIcs-SoCG-2016-35.pdf","access_level":"open_access","creator":"system","checksum":"cee65b0e722d50f9d1cc70c90ec1d59b","date_updated":"2020-07-14T12:44:47Z","relation":"main_file","file_id":"4699","date_created":"2018-12-12T10:08:38Z","content_type":"application/pdf","file_size":536923}],"page":"35.1 - 35.10","publist_id":"5833","doi":"10.4230/LIPIcs.SoCG.2016.35","_id":"1378","conference":{"location":"Medford, MA, USA","start_date":"2016-06-14","end_date":"2016-06-17","name":"SoCG: Symposium on Computational Geometry"},"date_updated":"2023-09-27T12:29:56Z","oa":1,"language":[{"iso":"eng"}],"publisher":"Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing","year":"2016","volume":51,"day":"01","pubrep_id":"623","publication_status":"published","department":[{"_id":"UlWa"}],"alternative_title":["LIPIcs"],"author":[{"full_name":"Dotterrer, Dominic","last_name":"Dotterrer","first_name":"Dominic"},{"first_name":"Tali","full_name":"Kaufman, Tali","last_name":"Kaufman"},{"full_name":"Wagner, Uli","last_name":"Wagner","first_name":"Uli","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"}],"intvolume":"        51","citation":{"ista":"Dotterrer D, Kaufman T, Wagner U. 2016. On expansion and topological overlap. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 51, 35.1-35.10.","ama":"Dotterrer D, Kaufman T, Wagner U. On expansion and topological overlap. In: Vol 51. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing; 2016:35.1-35.10. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2016.35\">10.4230/LIPIcs.SoCG.2016.35</a>","short":"D. Dotterrer, T. Kaufman, U. Wagner, in:, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2016, p. 35.1-35.10.","chicago":"Dotterrer, Dominic, Tali Kaufman, and Uli Wagner. “On Expansion and Topological Overlap,” 51:35.1-35.10. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2016. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2016.35\">https://doi.org/10.4230/LIPIcs.SoCG.2016.35</a>.","mla":"Dotterrer, Dominic, et al. <i>On Expansion and Topological Overlap</i>. Vol. 51, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2016, p. 35.1-35.10, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2016.35\">10.4230/LIPIcs.SoCG.2016.35</a>.","apa":"Dotterrer, D., Kaufman, T., &#38; Wagner, U. (2016). On expansion and topological overlap (Vol. 51, p. 35.1-35.10). Presented at the SoCG: Symposium on Computational Geometry, Medford, MA, USA: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2016.35\">https://doi.org/10.4230/LIPIcs.SoCG.2016.35</a>","ieee":"D. Dotterrer, T. Kaufman, and U. Wagner, “On expansion and topological overlap,” presented at the SoCG: Symposium on Computational Geometry, Medford, MA, USA, 2016, vol. 51, p. 35.1-35.10."},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"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 X → ℝd there exists a point p ∈ ℝd whose preimage intersects a positive fraction μ &gt; 0 of the d-cells of X. More generally, the conclusion holds if ℝd is replaced by any d-dimensional piecewise-linear (PL) manifold M, with a constant μ that depends only on d and on the expansion properties of X, but not on M.","lang":"eng"}],"project":[{"name":"Embeddings in Higher Dimensions: Algorithms and Combinatorics","grant_number":"PP00P2_138948","_id":"25FA3206-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","scopus_import":1,"related_material":{"record":[{"status":"public","id":"742","relation":"later_version"}]},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","has_accepted_license":"1","oa_version":"Published Version","date_created":"2018-12-11T11:51:41Z","file_date_updated":"2020-07-14T12:44:47Z","date_published":"2016-06-01T00:00:00Z","month":"06","type":"conference","ddc":["510"],"title":"On expansion and topological overlap","status":"public"}