{"isi":1,"year":"2019","date_updated":"2025-04-14T09:10:06Z","citation":{"chicago":"Avvakumov, Sergey, R. Karasev, and A. Skopenkov. “Stronger Counterexamples to the Topological Tverberg Conjecture.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.1908.08731\">https://doi.org/10.48550/arXiv.1908.08731</a>.","short":"S. Avvakumov, R. Karasev, A. Skopenkov, ArXiv (n.d.).","ama":"Avvakumov S, Karasev R, Skopenkov A. Stronger counterexamples to the topological Tverberg conjecture. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.1908.08731\">10.48550/arXiv.1908.08731</a>","ista":"Avvakumov S, Karasev R, Skopenkov A. Stronger counterexamples to the topological Tverberg conjecture. arXiv, 1908.08731.","ieee":"S. Avvakumov, R. Karasev, and A. Skopenkov, “Stronger counterexamples to the topological Tverberg conjecture,” <i>arXiv</i>. .","apa":"Avvakumov, S., Karasev, R., &#38; Skopenkov, A. (n.d.). Stronger counterexamples to the topological Tverberg conjecture. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.1908.08731\">https://doi.org/10.48550/arXiv.1908.08731</a>","mla":"Avvakumov, Sergey, et al. “Stronger Counterexamples to the Topological Tverberg Conjecture.” <i>ArXiv</i>, 1908.08731, doi:<a href=\"https://doi.org/10.48550/arXiv.1908.08731\">10.48550/arXiv.1908.08731</a>."},"oa_version":"Preprint","arxiv":1,"department":[{"_id":"UlWa"}],"article_processing_charge":"No","publication":"arXiv","date_published":"2019-08-23T00:00:00Z","author":[{"last_name":"Avvakumov","orcid":"0000-0002-7840-5062","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","first_name":"Sergey","full_name":"Avvakumov, Sergey"},{"full_name":"Karasev, R.","first_name":"R.","last_name":"Karasev"},{"first_name":"A.","full_name":"Skopenkov, A.","last_name":"Skopenkov"}],"project":[{"grant_number":"P31312","call_identifier":"FWF","name":"Algorithms for Embeddings and Homotopy Theory","_id":"26611F5C-B435-11E9-9278-68D0E5697425"}],"day":"23","title":"Stronger counterexamples to the topological Tverberg conjecture","acknowledgement":"We would like to thank F. Frick for helpful discussions","_id":"8184","article_number":"1908.08731","publication_status":"draft","external_id":{"isi":["000986519600004"],"arxiv":["1908.08731"]},"status":"public","type":"preprint","month":"08","date_created":"2020-07-30T10:45:34Z","main_file_link":[{"url":"https://arxiv.org/abs/1908.08731","open_access":"1"}],"oa":1,"doi":"10.48550/arXiv.1908.08731","language":[{"iso":"eng"}],"related_material":{"record":[{"id":"8156","relation":"dissertation_contains","status":"public"}]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"text":"Denote by ∆N the N-dimensional simplex. A map f : ∆N → Rd is an almost r-embedding if fσ1∩. . .∩fσr = ∅ whenever σ1, . . . , σr are pairwise disjoint faces. A counterexample to the topological Tverberg conjecture asserts that if r is not a prime power and d ≥ 2r + 1, then there is an almost r-embedding ∆(d+1)(r−1) → Rd. This was improved by Blagojevi´c–Frick–Ziegler using a simple construction of higher-dimensional counterexamples by taking k-fold join power of lower-dimensional ones. We improve this further (for d large compared to r): If r is not a prime power and N := (d+ 1)r−r l\r\nd + 2 r + 1 m−2, then there is an almost r-embedding ∆N → Rd. For the r-fold van Kampen–Flores conjecture we also produce counterexamples which are stronger than previously known. Our proof is based on generalizations of the Mabillard–Wagner theorem on construction of almost r-embeddings from equivariant maps, and of the Ozaydin theorem on existence of equivariant maps. ","lang":"eng"}]}