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Hurewicz-Serre theorem in extension theory
Cencelj, Matija, 1958- ...
Članek je posvečen posplošitvam izrekov Cenclja in Dranišnikova o zvezah med razširljivostnimi lastnostmi nilpotentnih CW kompleksov in njihovimi homološkimi grupami. Glavna rezultata članka sta ...naslednja izreka. Izrek 1: Naj bo ▫$L$▫ nilpotentni CW kompleks in ▫$F$▫ homotopsko vlakno inkluzije ▫$L$▫ v neskončni simetrični produkt SP(L). Če je ▫$X$▫ metrizabilen prostor, za katerega so ▫$X \tau K(H_k(L),k)$▫ absolutni ekstenzorji za ▫$X$▫ za vsak ▫$k \geq 1$▫, tedaj so tudi ▫$X \tau K(\pi_k(F),k)$▫ in ▫$X \tau K(\pi_k(L),k))$▫ absolutni ekstenzorji za vsak ▫$k \geq 2$▫. Izrek 2: Naj bo ▫$X$▫ metrizabilen prostor, ki je končno dimenzionalen ali pa ANR. Naj bo ▫$L$▫ nilpotentni CW kompleks. Če je SP(L) absolutni ekstenzor za ▫$X$▫, je tudi Labsolutni ekstenzor za ▫$X$▫ v naslednjih primerih. (a) ▫$H_1(L)$▫ je končno generiran. (b) ▫$H_1(L)$▫ je torzijska grupa.
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