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  • Simply connected 3-manifolds with a dense set of ends of specified genus
    Garity, Dennis, 1950- ; Repovš, Dušan, 1954-
    We show that for every sequence ▫$(n_i)$▫, where each ▫$n_i$▫ is either an integer greater than 1 or is ▫$\infty$▫, there exists a simply connected open 3-manifold ▫$M$▫ with a countable dense set of ... ends ▫$\{e_i\}$▫ so that, for every ▫$i$▫, the genus of end ▫$e_i$▫ is equal to ▫$n_i$▫. In addition, the genus of the ends not in the dense set is shown to be less than or equal to 2. These simply connected 3-manifolds are constructed as the complements of certain Cantor sets in ▫$S^3$▫. The methods used require careful analysis of the genera of ends and new techniques for dealing with infinite genus.
    Source: Mediterranean journal of mathematics. - ISSN 1660-5446 (Vol. 14, iss. 3, 2017, art. 109 (12 str.))
    Type of material - article, component part ; adult, serious
    Publish date - 2017
    Language - english
    COBISS.SI-ID - 18016345

    Link(s):

    http://dx.doi.org/10.1007/s00009-017-0907-9
    Repository of the University of Ljubljana – RUL

source: Mediterranean journal of mathematics. - ISSN 1660-5446 (Vol. 14, iss. 3, 2017, art. 109 (12 str.))
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