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

Hegenbarth, Friedrich (avtor), Repovš, Dušan (avtor)

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.

• Jezik: Angleški jezik
• Ključne besede: Poincaré duality complex, generalized manifold, Steenrod ▫$\mathbb{L}$▫-homology, periodic surgery spectrum ▫$\mathbb{L}$▫, fundamental complex, $\mathbb{L}$-homology class, Quinn index
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: PEF - Pedagoška fakulteta; FMF - Fakulteta za matematiko in fiziko
• Leto izida: 2020
• Št. strani: Str. 579-607
• Številčenje: Vol. 63, no. 2
• PID: 20.500.12556/RUL-116576
• UDK: 515.14
• ISSN pri članku: 0013-0915
• DOI: 10.1017/S0013091520000012
• COBISS.SI-ID: 18947417
• Datum objave v RUL: 28.05.2020

Gradivo je del revije

• Naslov: Proceedings of the Edinburgh Mathematical Society
• Skrajšan naslov: Proc. Edinb. Math. Soc.
• Založnik: Scottish Academic Press
• ISSN: 0013-0915
• COBISS.SI-ID: 27124480