Controlled surgery and $\mathbb{L}$-homology

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

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 $H_n(B,L) \to H_n(B, \, L_0)$.

• Jezik: Angleški jezik
• Ključne besede: generalized manifold, resolution obstruction, controlled surgery, controlled structure set, $\mathbb{L}_q$-surgery, Wall obstruction
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: PEF - Pedagoška fakulteta; FMF - Fakulteta za matematiko in fiziko
• Leto izida: 2019
• Št. strani: Str. 1-22
• Številčenje: art. 79, iss. 3
• PID: 20.500.12556/RUL-108784
• UDK: 515.1
• ISSN pri članku: 1660-5446
• DOI: 10.1007/s00009-019-1354-6
• COBISS.SI-ID: 18630745
• Datum objave v RUL: 25.07.2019

HEGENBARTH, Friedrich in REPOVŠ, Dušan, 2019, Controlled surgery and ▫$\mathbb{L}$▫-homology. Mediterranean journal of mathematics [na spletu]. 2019. Vol. 79, no. 3, p. 1–22. [Dostopano 21 april 2025]. DOI 10.1007/s00009-019-1354-6. Pridobljeno s: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=slv&id=108784

Gradivo je del revije

• Naslov: Mediterranean journal of mathematics
• Skrajšan naslov: Mediterr. j. math.
• Založnik: Springer Nature, University of Bari, Department of Mathematics
• ISSN: 1660-5446
• COBISS.SI-ID: 13561433