Friedrich Hegenbarth (Author), Dušan Repovš (Author)

Abstract

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.

Keywords

Poincaré duality complex;generalized manifold;Steenrod ▫$\mathbb{L}$▫-homology;periodic surgery spectrum ▫$\mathbb{L}$▫;fundamental complex;$\mathbb{L}$-homology class;Quinn index;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UL FMF - Faculty of Mathematics and Physics
UDC: 515.14
COBISS: 18947417 Link will open in a new window
ISSN: 0013-0915
Views: 465
Downloads: 242
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Other data

Type (COBISS): Article
Pages: str. 579-607
Volume: ǂVol. ǂ63
Issue: ǂno. ǂ2
Chronology: May 2020
DOI: 10.1017/S0013091520000012
ID: 11758057