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Montesinos Amilibia, José María ; González Acuña, Francisco Javier | Cambridge Univ. Press | 1982-05The authors show that every knot can be embedded in codimension two in a trivial knot, and they derive corresponding theorems about embedding branched coverings in codimension two. These results (and generalizations) were obtained previously by [...]texto impreso
In 1962, R. H. Fox asked [Topology of 3-manifolds and related topics (Proc. Univ. Georgia Inst., 1961), pp. 168–176, especially pp. 175–176, Prentice-Hall, Englewood Cliffs, N.J., 1962)] whether a 2-knot group could have infinitely many ends. Th[...]texto impreso
Montesinos Amilibia, José María ; González Acuña, Francisco Javier ; Birman, Joan S. | Michigan Mathematical Journal | 1976The authors construct an infinite family of prime homology 3-spheres of Heegaard genus 2, satisfying the following two non-uniqueness properties: (1) Each of the manifolds can be structured as the 2-fold cyclic branched cover over each of two in[...]texto impreso
Montesinos Amilibia, José María ; González Acuña, Francisco Javier | Canadian Mathematical Society | 1980-02-01An n-knot (Sn+2,Sn) is said to be amphicheiral if there is an orientation-reversing autohomeomorphism of Sn+2 which leaves Sn invariant as a set. An n-knot is said to be invertible if there is an orientation-preserving autohomeomorphism of Sn+2 [...]texto impreso
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Montesinos Amilibia, José María ; González Acuña, Francisco Javier | European Mathematical Society | 1983A smooth n-knot K in Sn+2 is said to be quasiaspherical if Hn+1(U)=0, where U is the universal cover of the exterior of K. Let G be the group of K and H the subgroup generated by a meridian. Then (G,H) is said to be unsplittable if G does not ha[...]texto impreso
Montesinos Amilibia, José María ; Boileau, Michel ; González Acuña, Francisco Javier | Springer | 1987-01W. Whitten conjectured [Pacific J. Math. 97 (1981), no. 1, 209–216] that no 3-manifold obtained by a nontrivial surgery on a double of a noninvertible knot is a 2-fold branched covering of S3. The authors give counterexamples to this conjecture [...]
