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The relationship of generalized manifolds to Poincaré duality complexes and topological manifolds
ID Hegenbarth, Friedrich (Avtor), ID Repovš, Dušan (Avtor)

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The primary purpose of this paper concerns the relation of (compact) generalized manifolds to finite Poincaré duality complexes (PD complexes). The problem is that an arbitrary generalized manifold X is always an ENR space, but it is not necessarily a complex. Moreover, finite PD complexes require the Poincaré duality with coefficients in the group ring Λ (Λ-complexes). Standard homology theory implies that X is a Z-PD complex. Therefore by Browder's theorem, X has a Spivak normal fibration which in turn, determines a Thom class of the pair (N,N) of a mapping cylinder neighborhood of X in some Euclidean space. Then X satisfies the Λ-Poincaré duality if this class induces an isomorphism with Λ-coefficients. Unfortunately, the proof of Browder's theorem gives only isomorphisms with Z-coefficients. It is also not very helpful that X is homotopy equivalent to a finite complex K, because K is not automatically a Λ-PD complex. Therefore it is convenient to introduce Λ-PD structures. To prove their existence on X, we use the construction of 2-patch spaces and some fundamental results of Bryant, Ferry, Mio, and Weinberger. Since the class of all Λ-PD complexes does not contain all generalized manifolds, we appropriately enlarge this class and then describe (i.e. recognize) generalized manifolds within this enlarged class in terms of the Gromov-Hausdorff metric.

Jezik:Angleški jezik
Ključne besede:generalized manifold, Poincaré duality complex, ENR, 2-patch space, resolution obstruction, controlled surgery, controlled structure set, Lq-surgery, Wall obstruction, cell-like map, Gromov-Hausdorff metric
Vrsta gradiva:Članek v reviji
Tipologija:1.01 - Izvirni znanstveni članek
Organizacija:PEF - Pedagoška fakulteta
FMF - Fakulteta za matematiko in fiziko
Leto izida:2018
Št. strani:Str. 126-141
Številčenje:Vol. 239
PID:20.500.12556/RUL-109104 Povezava se odpre v novem oknu
UDK:515.16
ISSN pri članku:0166-8641
DOI:10.1016/j.topol.2018.02.024 Povezava se odpre v novem oknu
COBISS.SI-ID:18273369 Povezava se odpre v novem oknu
Datum objave v RUL:22.08.2019
Število ogledov:1313
Število prenosov:542
Metapodatki:XML DC-XML DC-RDF
:
HEGENBARTH, Friedrich in REPOVŠ, Dušan, 2018, The relationship of generalized manifolds to Poincaré duality complexes and topological manifolds. Topology and its Applications [na spletu]. 2018. Vol. 239, p. 126–141. [Dostopano 19 februar 2025]. DOI 10.1016/j.topol.2018.02.024. Pridobljeno s: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=slv&id=109104
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Gradivo je del revije

Naslov:Topology and its Applications
Skrajšan naslov:Topol. appl.
Založnik:North-Holland
ISSN:0166-8641
COBISS.SI-ID:26538752 Povezava se odpre v novem oknu

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