Generalized manifolds, normal invariants, and L-homology

Friedrich Hegenbarth (Avtor), Dušan Repovš (Avtor)

Povzetek

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.

Ključne besede

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;

Podatki

Jezik:	Angleški jezik
Leto izida:	2021
Tipologija:	1.01 - Izvirni znanstveni članek
Organizacija:	UL FMF - Fakulteta za matematiko in fiziko
Založnik:	Cambridge University Press
UDK:	515.14
COBISS:	67730691
ISSN:	0013-0915
Št. ogledov:	200
Št. prenosov:	51
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Vrsta dela (COBISS):	Članek v reviji
Konec prepovedi (OpenAIRE):	2021-12-16
Strani:	str. 574-589
Letnik:	ǂVol. ǂ64
Zvezek:	ǂiss. ǂ3
Čas izdaje:	Aug. 2021
DOI:	10.1017/S0013091521000316
ID:	13582417