VSE knjižnice (vzajemna bibliografsko-kataložna baza podatkov COBIB.SI)
  • Inequivalent Cantor sets in ▫$R^3$▫ whose complements have the same fundamental group
    Garity, Dennis, 1950- ; Repovš, Dušan, 1954-
    For each Cantor set ▫$C$▫ in ▫$R^3$▫, all points of which have bounded local genus, we show that there are infinitely many inequivalent Cantor sets in ▫$R^3$▫ with the complement having the same ... fundamental group as the complement of T$C$T. This answers a question from "Open Problems in Topology" and has as anapplication a simple construction of nonhomeomorphic open -manifolds with the same fundamental group. The main techniques used are analysis of local genus of points of Cantor sets, a construction for producing rigid Cantor sets with simply connected complement, and manifold decomposition theory. The results presented give an argument that for certain groups ▫$G$▫, there are uncountably many nonhomeomorphic open 3-manifolds with fundamental group ▫$G$▫.
    Vir: Proceedings of the American Mathematical Society. - ISSN 0002-9939 (Vol. 141, no. 8, 2013, str. 2901-2911)
    Vrsta gradiva - članek, sestavni del
    Leto - 2013
    Jezik - angleški
    COBISS.SI-ID - 16636505

    Povezava(-e):

    http://dx.doi.org/10.1090/S0002-9939-2013-11911-8

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