Controlled surgery and ▫$\mathbb{L}$▫-homologyHegenbarth, Friedrich (Avtor) Repovš, Dušan (Avtor) generalized manifoldresolution obstructioncontrolled surgerycontrolled structure set▫$\mathbb{L}_q$▫-surgeryWall obstructionThis 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 ▫$H_n(B,L) \to H_n(B, \, L_0)$▫.20192019-07-25 07:42:04Članek v reviji108784sl