20.500.12556/RUL-108784 Controlled surgery and ▫$\mathbb{L}$▫-homology 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 ▫$H_n(B,L) \to H_n(B, \, L_0)$▫. generalized manifold resolution obstruction controlled surgery controlled structure set ▫$\mathbb{L}_q$▫-surgery Wall obstruction true false true Angleški jezik Ni določen Članek v reviji 2019-07-25 07:42:04 2019-07-25 07:42:08 2022-08-20 03:48:32 0000-00-00 00:00:00 2019 0 0 Str. 1-22 iss. 3 art. 79 June 2019 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 515.1 1660-5446 10.1007/s00009-019-1354-6 18630745 13561433 RAZ_Hegenbarth_Friedrich_i2019.pdf RAZ_Hegenbarth_Friedrich_i2019.pdf 1 B4039FC0A8975B4BB3134BE888456B5E 73b23cdac8d5053bf9a1d0c611b722f0579de333fb729ded89bc51604b1182f8 b9df5b05-a1b6-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=119892 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0