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▫${\cal F}$▫-vlaknenja in njihova klasifikacija : disertacija
Pavešić, Petar
Peter May je v knjigi Classifying spaces and fibrations predlagal zelo splošen pristop za opis vlaknatih prostorov s pomočjo kategorije ▫${\cal F}$▫ v kateri "živijo" njihova vlakna. Disertacija je ...posvečena posplošitvi osnovnih rezultatov o klasifikaciji vlaknenj na ▫${\cal F}$▫-vlaknenja. Najprej vpeljemo pojme kategorije vlaken ▫${\cal F}$▫, prirejene glavne kategorije vlaken ▫${\cal H}$▫, amalgamiranega produkta in kompletnega para kategorije vlaken, nato pa opišemo razširitev teh konstrukcij na vlaknate prostore. Klasifikacijo ▫${\cal F}$▫-vlaknenj dosežemo v dveh korakih: ob privzetku, da je ▫${\cal (F,H)}$▫ kompleten par vlaken, pokažemo, da je klasifikacija numerabilnih ▫${\cal F}$▫-vlaknenj ekvivalentna klasifikaciji glavnih numerabilnih ▫${\cal H}$▫-vlaknenj, nato pa konstruiramo klasifikacijski prostor za glavna numerabilna ▫${\cal H}$▫-vlaknenja. Z uporabo teh rezultatov izpeljemo posplošeno Gotliebovo formulo za klasifikacijski prostor homotopskih autoekvivalenc, ki ohranjajo bazno točko in podamo kriterije, kdaj je vlaknenje, katerega vlakno je produktivni prostor, vlaknati produkt dveh vlaknenj.
Type of material - dissertation
; adult, serious
Publication and manufacture - Ljubljana : [P. Pavešić], 1998
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