Povzetek

This paper presents an alternative approach to controlled surgery obstructions. The obstruction for a degree one normal map ▫$(f,b) \colon M^n \to X^n$▫ with control map ▫$q \colon X^n \to B$▫ to complete controlled surgery is an element ▫$\sigma^c (f,b) \in H_n(B, \mathbb{L})$▫, where ▫$M^n, \, X^n$▫ are topological manifolds of dimension ▫$n \ge 5$▫. Our proof uses essentially the geometrically defined ▫$\mathbb{L}$▫-spectrum as described by Nicas (going back to Quinn) and some well-known homotopy theory. We also outline the construction of the algebraically defined obstruction, and we explicitly describe the assembly map ▫$H_n(B,L) \to L_n(\pi_1(B))$▫ in terms of forms in the case ▫$n \equiv 0(4)$▫. Finally, we explicitly determine the canonical map ▫$H_n(B,L) \to H_n(B, \, L_0)$▫.

Ključne besede

generalized manifold;resolution obstruction;controlled surgery;controlled structure set;▫$\mathbb{L}_q$▫-surgery;Wall obstruction;

Podatki

Jezik: Angleški jezik
Leto izida:
Tipologija: 1.01 - Izvirni znanstveni članek
Organizacija: UL FMF - Fakulteta za matematiko in fiziko
UDK: 515.1
COBISS: 18630745 Povezava se bo odprla v novem oknu
ISSN: 1660-5446
Št. ogledov: 532
Št. prenosov: 220
Ocena: 0 (0 glasov)
Metapodatki: JSON JSON-RDF JSON-LD TURTLE N-TRIPLES XML RDFA MICRODATA DC-XML DC-RDF RDF

Ostali podatki

Vrsta dela (COBISS): Članek v reviji
Strani: art. 79 (22 str.)
Letnik: ǂVol. ǂ16
Zvezek: ǂiss. ǂ3
Čas izdaje: June 2019
DOI: 10.1007/s00009-019-1354-6
ID: 11193862