Smooth $2$-knots in $S\sp 2\times S\sp 2$ with simply-connected complements are topologically unique
نویسندگان
چکیده
منابع مشابه
Smooth Surfaces with Non-simply-connected Complements
We give two constructions of surfaces in simply-connected 4-manifolds with non simply-connected complements. One is an iteration of the twisted rim surgery introduced by the first author [7]. We also construct, for any group G satisfying some simple conditions, a simply-connected symplectic manifold containing a symplectic surface whose complement has fundamental group G. In each case, we produ...
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Vidussi was the first to construct knotted Lagrangian tori in simply connected four dimensional manifolds. Fintushel and Stern introduced a second way to detect such knotting. This note demonstrates that similar examples may be distinguished by the fundamental group of the exterior.
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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...
متن کاملKnots Are Determined by Their Complements
This answers a question apparently first raised by Tietze [T, p. 83]. It was previously known that there were at most two knots with a given complement [CGLS, Corollary 3]. 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 I holds in...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1989
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1989-0940880-x