20.500.12556/RUL-132482 Generalized manifolds, normal invariants, and L-homology Let ▫$X^{n}$▫ be an oriented closed generalized ▫$n$▫-manifold, ▫$n\ge 5$▫. In our recent paper (Proc. Edinb. Math. Soc. (2) 63 (2020), no. 2, 597-607), we have constructed a map ▫$t:\mathcal{N}(X^{n}) \to H^{st}_{n} ( X^{n}; \mathbb{L}^{+})$▫ which extends the normal invariant map for the case when ▫$X^{n}$▫ is a topological ▫$n$▫-manifold. Here, ▫$\mathcal{N}(X^{n})$▫ denotes the set of all normal bordism classes of degree one normal maps ▫$(f,\,b): M^{n} \to X^{n}$▫, and ▫$H^{st}_{*} ( X^{n}; \mathbb{E})$▫ denotes the Steenrod homology of the spectrum ▫$\mathbb{E}$▫. An important non-trivial question arose whether the map ▫$t$▫ is bijective (note that this holds in the case when ▫$X^{n}$▫ is a topological ▫$n$▫-manifold). It is the purpose of this paper to prove that the answer to this question is affirmative. generalized manifold Steenrod ▫$\mathbb{L}$▫-homology Poincaré duality complex normal invariant of degree one map periodic surgery spectrum ▫$\mathbb{L}$▫ fundamental complex Spivak fibration Pontryagin-Thom construction Spanier-Whitehead duality absolute neighbourhood retract true false true Cambridge University Press Angleški jezik Ni določen Članek v reviji 2021-10-27 11:13:47 2021-10-27 11:13:49 2022-09-12 04:12:36 0000-00-00 00:00:00 2021 0 0 Str. 574-589 Iss. 3 Vol. 64 Aug. 2021 0000-00-00 PostprintKoncna NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 2021-12-16 515.14 0013-0915 10.1017/S0013091521000316 67730691 RUL_verzija.pdf RUL_verzija.pdf 1 8562D8CB7BC06EFEA3CE2B19345E2E5D a88d82ac0ec049fb82077d4f8d46fbf5488e0a17bda6583649cfaa31da826efe 2c8e120f-f76d-11ec-8aca-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=157751 https://doi.org/10.1017/S0013091521000316 0 570b9c37-3706-11ec-abdb-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=150133 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0