Serrova vlaknenja v Morita kategoriji topoloških grupoidov : doktorska disertacija
Jelenc, Blaž, 1981-
V disertaciji obravnavamo homotopsko teorijo topoloških grupoidov. Delamo z opisom homotopskih grup topoloških grupoidov, ki predstavi homotopske grupe topološkega grupoida kot grupo homotopskih ...razredov glavnih svežnjev. Pokažemo, da se te homotopske grupe ujemajo z običajnimi homotopskimi grupami klasifikacijskega prostora prirejenega topološkemu grupoidu. Nato uvedemo posplošitev klasičnega Serrovega vlaknenja na Morita kategorijo topoloških grupoidov, ogledamo si razne lastnosti Serrovih vlaknenj in izpeljemo dolgo eksaktno zaporedje homotopskih grup grupoidov, ki ga to Serrovo vlaknenje inducira. V nadaljevanju si ogledamo najprej več primerov Serrovih vlaknenj, nato pa še razred Serrovih grupoidov, ki zaobsega dokaj velik del grupoidov, ki se pojavljajo v praksi. Nazadnje predstavimo še posplošitev obravnavanih homotopskih grup na homotopske grupe ▫$K$▫-označenih grupoidov, kjer je ▫$K$▫ topološka grupa. Rezultate nato uporabimo za analizo prezentabilnosti pravih regularnih Lijevih grupoidov.
Type of material - dissertation
; adult, serious
Publication and manufacture - Ljubljana : [B. Jelenc], 2013
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