{"issue":"3","extern":"1","publication_status":"published","date_published":"2021-10-01T00:00:00Z","abstract":[{"text":"Suppose that n is not a prime power and not twice a prime power. We prove that for any Hausdorff compactum X with a free action of the symmetric group Sn, there exists an Sn-equivariant map X→Rn whose image avoids the diagonal {(x,x,…,x)∈Rn∣x∈R}. Previously, the special cases of this statement for certain X were usually proved using the equivartiant obstruction theory. Such calculations are difficult and may become infeasible past the first (primary) obstruction. We take a different approach which allows us to prove the vanishing of all obstructions simultaneously. The essential step in the proof is classifying the possible degrees of Sn-equivariant maps from the boundary ∂Δn−1 of (n−1)-simplex to itself. Existence of equivariant maps between spaces is important for many questions arising from discrete mathematics and geometry, such as Kneser’s conjecture, the Square Peg conjecture, the Splitting Necklace problem, and the Topological Tverberg conjecture, etc. We demonstrate the utility of our result applying it to one such question, a specific instance of envy-free division problem.","lang":"eng"}],"day":"01","type":"journal_article","date_updated":"2023-02-23T13:26:41Z","article_processing_charge":"No","month":"10","related_material":{"record":[{"status":"public","id":"8182","relation":"earlier_version"}]},"status":"public","quality_controlled":"1","title":"Vanishing of all equivariant obstructions and the mapping degree","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2022-06-17T08:45:15Z","oa_version":"Preprint","scopus_import":"1","publisher":"Springer Nature","citation":{"short":"S. Avvakumov, S. Kudrya, Discrete &#38; Computational Geometry 66 (2021) 1202–1216.","ista":"Avvakumov S, Kudrya S. 2021. Vanishing of all equivariant obstructions and the mapping degree. Discrete &#38; Computational Geometry. 66(3), 1202–1216.","apa":"Avvakumov, S., &#38; Kudrya, S. (2021). Vanishing of all equivariant obstructions and the mapping degree. <i>Discrete &#38; Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-021-00299-z\">https://doi.org/10.1007/s00454-021-00299-z</a>","chicago":"Avvakumov, Sergey, and Sergey Kudrya. “Vanishing of All Equivariant Obstructions and the Mapping Degree.” <i>Discrete &#38; Computational Geometry</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00454-021-00299-z\">https://doi.org/10.1007/s00454-021-00299-z</a>.","ama":"Avvakumov S, Kudrya S. Vanishing of all equivariant obstructions and the mapping degree. <i>Discrete &#38; Computational Geometry</i>. 2021;66(3):1202-1216. doi:<a href=\"https://doi.org/10.1007/s00454-021-00299-z\">10.1007/s00454-021-00299-z</a>","ieee":"S. Avvakumov and S. Kudrya, “Vanishing of all equivariant obstructions and the mapping degree,” <i>Discrete &#38; Computational Geometry</i>, vol. 66, no. 3. Springer Nature, pp. 1202–1216, 2021.","mla":"Avvakumov, Sergey, and Sergey Kudrya. “Vanishing of All Equivariant Obstructions and the Mapping Degree.” <i>Discrete &#38; Computational Geometry</i>, vol. 66, no. 3, Springer Nature, 2021, pp. 1202–16, doi:<a href=\"https://doi.org/10.1007/s00454-021-00299-z\">10.1007/s00454-021-00299-z</a>."},"article_type":"original","language":[{"iso":"eng"}],"_id":"11446","page":"1202-1216","doi":"10.1007/s00454-021-00299-z","author":[{"id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","full_name":"Avvakumov, Sergey","first_name":"Sergey","last_name":"Avvakumov"},{"last_name":"Kudrya","first_name":"Sergey","id":"ecf01965-d252-11ea-95a5-8ada5f6c6a67","full_name":"Kudrya, Sergey"}],"publication":"Discrete & Computational Geometry","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"external_id":{"arxiv":["1910.12628"]},"acknowledgement":"S. Avvakumov has received funding from the European Research Council under the European Union’s Seventh Framework Programme ERC Grant agreement ERC StG 716424–CASe. S. Kudrya was supported by the Austrian Academic Exchange Service (OeAD), ICM-2019-13577.","keyword":["Computational Theory and Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Theoretical Computer Science"],"volume":66,"intvolume":"        66","year":"2021"}