V članku proučujemo različne koncepte periferne acikličnosti in lokalnih homotopskih lastnosti ter posplošimo in razširimo prejšnje rezultate R.C. Lacherja, D.R.McMillana, Jr. ter obeh avtorjev. Nato ...dobimo nekaj uporabnih rezultatov za celičaste dekompozicije mnogoterosti in konstruiramo eksotične faktorje (t.j. homološke mnogoterosti) za nekatere evklidske prostore.
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