Generalized manifolds, normal invariants, and L-homologyHegenbarth, Friedrich (Avtor) Repovš, Dušan (Avtor) generalized manifoldSteenrod ▫$\mathbb{L}$▫-homologyPoincaré duality complexnormal invariant of degreeone mapperiodic surgery spectrum ▫$\mathbb{L}$▫fundamental complexSpivak fibrationPontryagin-Thom constructionSpanier-Whitehead dualityabsolute neighbourhood retractLet ▫$X^{n}$▫ 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.Cambridge University Press20212021-10-27 11:13:47Članek v reviji132482UDK: 515.14ISSN pri članku: 0013-0915DOI: 10.1017/S0013091521000316COBISS_ID: 67730691sl