On Steenrod $\mathbb{L}$-homology, generalized manifolds, and surgery

Hegenbarth, Friedrich (author), Repovš, Dušan (author)

The aim of this paper is to show the importance of the Steenrod construction of homology theories for the disassembly process in surgery on a generalized $n$-manifold $X^n$, in order to produce an element of generalized homology theory, which is basic for calculations. In particular, we show how to construct an element of the $n$th Steenrod homology group $H^{st}_n (X^n, \mathbb{L}^+)$, where $\mathbb{L}^+$ is the connected covering spectrum of the periodic surgery spectrum $\mathbb{L}$, avoiding the use of the geometric splitting procedure, the use of which is standard in surgery on topological manifolds.

• Language: English
• Keywords: Poincaré duality complex, generalized manifold, Steenrod $\mathbb{L}$-homology, periodic surgery spectrum $\mathbb{L}$, fundamental complex, $\mathbb{L}$-homology class, Quinn index
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2020
• Number of pages: Str. 579-607
• Numbering: Vol. 63, no. 2
• PID: 20.500.12556/RUL-116576
• UDC: 515.14
• ISSN on article: 0013-0915
• DOI: 10.1017/S0013091520000012
• COBISS.SI-ID: 18947417
• Publication date in RUL: 28.05.2020

HEGENBARTH, Friedrich and REPOVŠ, Dušan, 2020, On Steenrod ▫$\mathbb{L}$▫-homology, generalized manifolds, and surgery. Proceedings of the Edinburgh Mathematical Society [online]. 2020. Vol. 63, no. 2, p. 579–607. [Accessed 15 August 2025]. DOI 10.1017/S0013091520000012. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=116576

Record is a part of a journal

• Title: Proceedings of the Edinburgh Mathematical Society
• Shortened title: Proc. Edinb. Math. Soc.
• Publisher: Scottish Academic Press
• ISSN: 0013-0915
• COBISS.SI-ID: 27124480