Geometric limits of knot complements, II: graphs determined by their complements
نویسندگان
چکیده
منابع مشابه
Geometric Limits of Knot Complements
We prove that any complete hyperbolic 3–manifold with finitely generated fundamental group, with a single topological end, and which embeds into S is the geometric limit of a sequence of hyperbolic knot complements in S. In particular, we derive the existence of hyperbolic knot complements which contain balls of arbitrarily large radius. We also show that a complete hyperbolic 3–manifold with t...
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The surgery theory of Browder, Lashof and Shaneson reduces the study of high-dimensional smooth knots n , ! S n+2 with 1 = Zto homotopy theory. We apply Williams's Poincar e embedding theorem to the unstable normal invariant : S n+2 ? ! (M=@M) of a Seifert surface M n+1 , ! S n+2. Then a knot is determined by its complement if the Z-cover of the complement is (n + 2)=3]-connected; we improve Fa...
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If L1 and L2 are two Brunnian links with all pairwise linking numbers 0, then we show that L1 and L2 are equivalent if and only if they have homeomorphic complements. In particular, this holds for all Brunnian links with at least three components. If L1 is a Brunnian link with all pairwise linking numbers 0, and the complement of L2 is homeomorphic to the complement of L1 , then we show that L2...
متن کاملKnots Are Determined by Their Complements
The notion of equivalence of knots can be strengthened by saying that K and K' are isotopic if the above homeomorphism h is isotopic to the identity, or equivalently, orientation-preserving. The analog of Theorem 1 holds in this setting too: if two knots have complements which are homeomorphic by an orientation-preserving homeomorphism, then they are isotopic. Theorem 1 and its orientation-pres...
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2011
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-011-0877-8