The Arf-Kervaire invariant of framed manifolds as an obstruction to embeddability

Ahmetʹev, Petr Mihajlovič (author), Cencelj, Matija (author), Repovš, Dušan (author)

We prove that no 14-connected (resp. 30-connected) stably parallelizable manifold ▫$N^{30}$▫ (resp. ▫$N^{62}$▫) of dimension 30 (resp. 62) with the Arf-Kervaire invariant 1 can be smoothly embedded into ▫$\mathbb{R}^{36}$▫ (resp. ▫$\mathbb{R}^{83}$▫).

• Language: English
• Keywords: Arf-Kervaire invariant, manifold, embeddability
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2022
• Number of pages: 17 str.
• Numbering: Vol. 100, no. 2, art. A10
• PID: 20.500.12556/RUL-143422
• UDC: 515.145.8
• ISSN on article: 1825-1242
• DOI: 10.1478/AAPP.1002A10
• COBISS.SI-ID: 133235715
• Publication date in RUL: 20.12.2022

Record is a part of a journal

• Title: Atti della Accademia Peloritana dei Pericolanti. Classe di Scienze Fisiche, Matemàtiche e Naturali
• Shortened title: Atti Accad. Pelorit. Pericol., Cl. Sci. Fis. Mat. Nat.
• Publisher: Accademia Peloritana dei Pericolanti
• ISSN: 1825-1242
• COBISS.SI-ID: 517583385

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.