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: |
2019 |
Tipologija: |
1.01 - Izvirni znanstveni članek |
Organizacija: |
UL FMF - Fakulteta za matematiko in fiziko |
UDK: |
515.1 |
COBISS: |
18630745
|
ISSN: |
1660-5446 |
Št. ogledov: |
532 |
Št. prenosov: |
220 |
Ocena: |
0 (0 glasov) |
Metapodatki: |
|
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 |