{"intvolume":"        16","acknowledgement":"I thank A. Skopenkov for telling me about the problem and for his useful remarks.  I also thank A. Sossinsky,\r\nA. Zhubr, M. Skopenkov, P. Akhmetiev, and an anonymous referee for their feedback.  Author was partially\r\nsupported by Dobrushin fellowship, 2013, and by RFBR grant 15-01-06302.","article_type":"original","oa":1,"oa_version":"Preprint","publication_status":"published","type":"journal_article","year":"2016","author":[{"last_name":"Avvakumov","full_name":"Avvakumov, Serhii","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","first_name":"Serhii"}],"_id":"1522","title":"The classification of certain linked 3-manifolds in 6-space","department":[{"_id":"UlWa"}],"date_created":"2018-12-11T11:52:30Z","volume":16,"month":"01","page":"1 - 25","date_updated":"2022-02-25T10:15:57Z","publisher":"Independent University of Moscow","abstract":[{"lang":"eng","text":"We classify smooth Brunnian (i.e., unknotted on both components) embeddings (S2 × S1) ⊔ S3 → ℝ6. Any Brunnian embedding (S2 × S1) ⊔ S3 → ℝ6 is isotopic to an explicitly constructed embedding fk,m,n for some integers k, m, n such that m ≡ n (mod 2). Two embeddings fk,m,n and fk′ ,m′,n′ are isotopic if and only if k = k′, m ≡ m′ (mod 2k) and n ≡ n′ (mod 2k). We use Haefliger’s classification of embeddings S3 ⊔ S3 → ℝ6 in our proof. The relation between the embeddings (S2 × S1) ⊔ S3 → ℝ6 and S3 ⊔ S3 → ℝ6 is not trivial, however. For example, we show that there exist embeddings f: (S2 ×S1) ⊔ S3 → ℝ6 and g, g′ : S3 ⊔ S3 → ℝ6 such that the componentwise embedded connected sum f # g is isotopic to f # g′ but g is not isotopic to g′."}],"publist_id":"5652","issue":"1","language":[{"iso":"eng"}],"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":"1","doi":"10.17323/1609-4514-2016-16-1-1-25","citation":{"mla":"Avvakumov, Sergey. “The Classification of Certain Linked 3-Manifolds in 6-Space.” <i>Moscow Mathematical Journal</i>, vol. 16, no. 1, Independent University of Moscow, 2016, pp. 1–25, doi:<a href=\"https://doi.org/10.17323/1609-4514-2016-16-1-1-25\">10.17323/1609-4514-2016-16-1-1-25</a>.","ista":"Avvakumov S. 2016. The classification of certain linked 3-manifolds in 6-space. Moscow Mathematical Journal. 16(1), 1–25.","short":"S. Avvakumov, Moscow Mathematical Journal 16 (2016) 1–25.","apa":"Avvakumov, S. (2016). The classification of certain linked 3-manifolds in 6-space. <i>Moscow Mathematical Journal</i>. Independent University of Moscow. <a href=\"https://doi.org/10.17323/1609-4514-2016-16-1-1-25\">https://doi.org/10.17323/1609-4514-2016-16-1-1-25</a>","ieee":"S. Avvakumov, “The classification of certain linked 3-manifolds in 6-space,” <i>Moscow Mathematical Journal</i>, vol. 16, no. 1. Independent University of Moscow, pp. 1–25, 2016.","ama":"Avvakumov S. The classification of certain linked 3-manifolds in 6-space. <i>Moscow Mathematical Journal</i>. 2016;16(1):1-25. doi:<a href=\"https://doi.org/10.17323/1609-4514-2016-16-1-1-25\">10.17323/1609-4514-2016-16-1-1-25</a>","chicago":"Avvakumov, Sergey. “The Classification of Certain Linked 3-Manifolds in 6-Space.” <i>Moscow Mathematical Journal</i>. Independent University of Moscow, 2016. <a href=\"https://doi.org/10.17323/1609-4514-2016-16-1-1-25\">https://doi.org/10.17323/1609-4514-2016-16-1-1-25</a>."},"status":"public","day":"01","publication_identifier":{"eissn":["1609-4514"]},"date_published":"2016-01-01T00:00:00Z","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1408.3918"}],"quality_controlled":"1","external_id":{"arxiv":["1408.3918"]},"publication":"Moscow Mathematical Journal"}