On the problems of determining knots by their complements and knot complements by their groups
نویسندگان
چکیده
منابع مشابه
KNOTS DETERMINED BY THEIR COMPLEMENTS 3 Proof
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...
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...
متن کاملBrunnian links are determined by their complements
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 کاملON THE STRUCTURE OF FINITE PSEUDO- COMPLEMENTS OF QUADRILATERALS AND THEIR EMBEDDABILITY
A pseudo-complement of a quadrilateral D of order n, n, > 3, is a non-trivial (n+l)- regular linear space with n - 3n + 3 points and n + n - 3 lines. We prove that if n > 18 and D has at least one line of size n - 1, or if n > 25 , then the set of lines of D consists of three lines of size n -1, 6(n - 2) lines of size n - 2, and n - 5n + 6 lines of size n - 3. Furthermore, if n > 21 and D...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1976
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1976-0402719-1