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  • The geometry and fundamental groups of solenoid complements
    Conner, Gregory R. ; Meilstrup, Mark H., 1980- ; Repovš, Dušan, 1954-
    A solenoid is an inverse limit of circles. When a solenoid is embedded in three space, its complement is an open three manifold. We discuss the geometry and fundamental groups of such manifolds, and ... show that the complements of different solenoids (arising from different inverse limits) have different fundamental groups. Embeddings of the same solenoid can give different groups; in particular, the nicest embeddings are unknotted at each level, and give an Abelian fundamental group, while other embeddings have non-Abelian groups. We show using geometry that every solenoid has uncountably many embeddings with nonhomeomorphic complements.
    Source: Journal of knot theory and its ramifications. - ISSN 0218-2165 (Vol. 24, iss. 14, 2015, 20 str.)
    Type of material - article, component part ; adult, serious
    Publish date - 2015
    Language - english
    COBISS.SI-ID - 17540697

    Link(s):

    http://dx.doi.org/10.1142/S0218216515500698
    Repository of the University of Ljubljana – RUL
    DOI

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