--- _id: '1381' abstract: - lang: eng text: 'Motivated by Tverberg-type problems in topological combinatorics and by classical results about embeddings (maps without double points), we study the question whether a finite simplicial complex K can be mapped into double-struck Rd without higher-multiplicity intersections. We focus on conditions for the existence of almost r-embeddings, i.e., maps f : K → double-struck Rd such that f(σ1) ∩ ⋯ ∩ f(σr) = ∅ whenever σ1, ..., σr are pairwise disjoint simplices of K. Generalizing the classical Haefliger-Weber embeddability criterion, we show that a well-known necessary deleted product condition for the existence of almost r-embeddings is sufficient in a suitable r-metastable range of dimensions: If rd ≥ (r + 1) dim K + 3, then there exists an almost r-embedding K → double-struck Rd if and only if there exists an equivariant map (K)Δ r → Sr Sd(r-1)-1, where (K)Δ r is the deleted r-fold product of K, the target Sd(r-1)-1 is the sphere of dimension d(r - 1) - 1, and Sr is the symmetric group. This significantly extends one of the main results of our previous paper (which treated the special case where d = rk and dim K = (r - 1)k for some k ≥ 3), and settles an open question raised there.' alternative_title: - LIPIcs author: - first_name: Isaac full_name: Mabillard, Isaac id: 32BF9DAA-F248-11E8-B48F-1D18A9856A87 last_name: Mabillard - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 citation: ama: 'Mabillard I, Wagner U. Eliminating higher-multiplicity intersections, II. The deleted product criterion in the r-metastable range. In: Vol 51. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH; 2016:51.1-51.12. doi:10.4230/LIPIcs.SoCG.2016.51' apa: 'Mabillard, I., & Wagner, U. (2016). Eliminating higher-multiplicity intersections, II. The deleted product criterion in the r-metastable range (Vol. 51, p. 51.1-51.12). Presented at the SoCG: Symposium on Computational Geometry, Medford, MA, USA: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH. https://doi.org/10.4230/LIPIcs.SoCG.2016.51' chicago: Mabillard, Isaac, and Uli Wagner. “Eliminating Higher-Multiplicity Intersections, II. The Deleted Product Criterion in the r-Metastable Range,” 51:51.1-51.12. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, 2016. https://doi.org/10.4230/LIPIcs.SoCG.2016.51. ieee: 'I. Mabillard and U. Wagner, “Eliminating higher-multiplicity intersections, II. The deleted product criterion in the r-metastable range,” presented at the SoCG: Symposium on Computational Geometry, Medford, MA, USA, 2016, vol. 51, p. 51.1-51.12.' ista: 'Mabillard I, Wagner U. 2016. Eliminating higher-multiplicity intersections, II. The deleted product criterion in the r-metastable range. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 51, 51.1-51.12.' mla: Mabillard, Isaac, and Uli Wagner. Eliminating Higher-Multiplicity Intersections, II. The Deleted Product Criterion in the r-Metastable Range. Vol. 51, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, 2016, p. 51.1-51.12, doi:10.4230/LIPIcs.SoCG.2016.51. short: I. Mabillard, U. Wagner, in:, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, 2016, p. 51.1-51.12. conference: end_date: 2016-06-17 location: Medford, MA, USA name: 'SoCG: Symposium on Computational Geometry' start_date: 2016-06-14 date_created: 2018-12-11T11:51:41Z date_published: 2016-06-01T00:00:00Z date_updated: 2021-01-12T06:50:17Z day: '01' ddc: - '510' department: - _id: UlWa doi: 10.4230/LIPIcs.SoCG.2016.51 file: - access_level: open_access checksum: 92c0c3735fe908f8ded6e484005cb3b1 content_type: application/pdf creator: system date_created: 2018-12-12T10:10:06Z date_updated: 2020-07-14T12:44:47Z file_id: '4791' file_name: IST-2016-621-v1+1_LIPIcs-SoCG-2016-51.pdf file_size: 622969 relation: main_file file_date_updated: 2020-07-14T12:44:47Z has_accepted_license: '1' intvolume: ' 51' language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ month: '06' oa: 1 oa_version: Published Version page: 51.1 - 51.12 project: - _id: 25FA3206-B435-11E9-9278-68D0E5697425 grant_number: PP00P2_138948 name: 'Embeddings in Higher Dimensions: Algorithms and Combinatorics' publication_status: published publisher: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH publist_id: '5830' pubrep_id: '621' quality_controlled: '1' scopus_import: 1 status: public title: Eliminating higher-multiplicity intersections, II. The deleted product criterion in the r-metastable range tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 51 year: '2016' ...