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Reducibility of self-homotopy equivalences
Pavešić, Petar
V članku opišemo novo in zelo splošno metodo za računanje grupe homotopskih avtoekvivalenc ▫$\mathrm{Aut}(X)$▫ prostora ▫$X$▫. Osnova za razcep grupe ▫$\mathrm{Aut}(X)$▫ je predstavitev ▫$X$▫ kot ...produkta preprostejših prostorov. Doslej so pri tem pristopu vedno nastopali privzetki, ki so bili precej omejevalni in težko ugotovljivi. V našem delu smo izpeljali preproste in izračunljive homoloske kriterije za tako imenovano reducibilnost preslikav, potem pa pokažemo, da je ta zahteva izpolnjena v primeru atomičnih razcepov. Na ta način je izračun ▫$\mathrm{Aut}(X)$▫ preveden na računanje grupe avtoekvivalenc faktorjev in množic homotopskih razredov preslikav med faktorji.
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