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A characterization of 2-knots groups.

Francisco González-Acuña — 1994

Revista Matemática Iberoamericana

A n-knot group is the fundamental group of the complement of an n-sphere smoothly embedded in Sⁿ⁺². Artin gave in 1925 ([A]) an algebraic characterization of 1-knot groups. M. Kervaire gave in 1965 ([K]) an algebraic characterization of n-knot groups for n ≥ 3. The problem of characterizing algebraically 2-knot groups has been posed several times (see for example [Su, Problem 4.7]). Ribbon 2-knot groups have been characterized algebraically by Yajima [Y]. We will...

Cyclic branched coverings of knots and homology spheres.

Francisco González-Acuña; Hamish Short — 1991

Revista Matemática de la Universidad Complutense de Madrid

We study cyclic coverings of S3 branched over a knot, and study conditions under which the covering is a homology sphere. We show that the sequence of orders of the first homology groups for a given knot is either periodic of tends to infinity with the order of the covering, a result recently obtained independently by Riley. From our computations it follows that, if surgery on a knot k with less than 10 crossings produces a manifold with cyclic fundamental group, then k is a torus knot.

Active sums I.

J. Alejandro Díaz-Barriga; Francisco González-Acuña; Francisco Marmolejo; Leopoldo Román — 2004

Revista Matemática Complutense

Given a generating family F of subgroups of a group G closed under conjugation and with partial order compatible with inclusion, a new group S can be constructed, taking into account the multiplication in the subgroups and their mutual actions given by conjugation. The group S is called the active sum of F, has G as a homomorph and is such that S/Z(S) ≅ G/Z(G) where Z denotes the center. The basic question we investigate in this paper...

On the homological category of 3-manifolds.

José Carlos Gómez Larrañaga; Francisco Javier González Acuña — 1991

Revista Matemática de la Universidad Complutense de Madrid

Let M be a closed, connected, orientable 3-manifold. Denote by n(S1 x S2) the connected sum of n copies of S1 x S2. We prove that if the homological category of M is three then for some n ≥ 1, H*(M) is isomorphic (as a ring) to H*(n(S1 x S2)).

On the homeotopy group of the non orientable surface of genus three.

González–Acuña, Francisco Javier; Márquez–Bobadilla, Juan Manuel — 2006

Revista Colombiana de Matemáticas

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