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  • Homogeneity groups of ends of open 3-manifolds

    Creator:
    Garity, Dennis J. and Repovš, Dušan
    Abstract:
    For every finitely generated abelian group G, we construct an irreducible open 3-manifold M[subscript G] whose end set is homeomorphic to a Cantor set and whose homogeneity group is isomorphic to G. The end homogeneity group is the group of self-homeomorphisms of the end set that extend to homeomorphisms of...
    Resource Type:
    Article
    Full Text:
    .2014.269.99 HOMOGENEITY GROUPS OF ENDS OF OPEN 3-MANIFOLDS DENNIS J. GARITY AND DUŠAN REPOVŠ For every

  • Inequivalent Cantor sets in 𝑅³ whose complements have the same fundamental group

    Creator:
    Garity, Dennis J. and Repovš, Dušan
    Abstract:
    For each Cantor set C in R³, all points of which have bounded local genus, we show that there are infinitely many inequivalent Cantor sets in R³ with the complement having the same fundamental group as the complement of C. This answers a question from Open Problems in Topology and...
    Resource Type:
    Article
    Full Text:
    INEQUIVALENT CANTOR SETS IN R3 WHOSE COMPLEMENTS HAVE THE SAME FUNDAMENTAL GROUP DENNIS J. GARITY AND DUŠAN

  • Simply connected open 3-manifolds with rigid genus one ends

    Creator:
    Garity, Dennis, Repovš, Dušan, and Wright, David
    Abstract:
    We construct uncountably many simply connected open 3-manifolds with genus one ends homeomorphic to the Cantor set. Each constructed manifold has the property that any self homeomorphism of the manifold (which necessarily extends to a homeomorphism of the ends) fixes the ends pointwise. These manifolds are complements of rigid generalized...
    Resource Type:
    Article
    Full Text:
    , DUŠAN REPOVŠ, AND DAVID WRIGHT Abstract. We construct uncountably many simply connected open 3