EUDML

We study the relation between the concept of spine and the representation of orientable bordered 3-manifolds by Heegaard diagrams. As a consequence, we show that composing invertible non-amphicheiral knots yields examples of topologically different knot manifolds with isomorphic spines. These results are related to some questions listed in [9], [11] and recover the main theorem of [10] as a corollary. Finally, an application concerning knot manifolds of composite knots with h prime factors completes...

On pseudo-isotopy classes of homeomorphisms of a dimensional differentiable manifold.

Alberto Cavicchioli; Friedrich Hegenbarth — 1998

Revista Matemática Complutense

We study self-homotopy equivalences and diffeomorphisms of the (n+1)-dimensional manifold X= #p(S1 x Sn) for any n ≥ 3. Then we completely determine the group of pseudo-isotopy classes of homeomorphisms of X and extend to dimension n well-known theorems due to F. Laudenbach and V. Poenaru (1972,1973), and J. M. Montesinos (1979).

On the intersection forms of closed 4-manifolds.

Alberto Cavicchioli; Friedrich Hegenbarth — 1992

Publicacions Matemàtiques

Given a closed 4-manifold M, let M* be the simply-connected 4-manifold obtained from M by killing the fundamental group. We study the relation between the intersection forms λ and λ. Finally some topological consequences and examples are described.

On the topological structure of compact 5-manifolds

Alberto Cavicchioli; Fulvia Spaggiari — 1993

Commentationes Mathematicae Universitatis Carolinae

We classify the genus one compact (PL) 5-manifolds and prove some results about closed 5-manifolds with free fundamental group. In particular, let $M$ be a closed connected orientable smooth $5$ -manifold with free fundamental group. Then we prove that the number of distinct smooth $5$ -manifolds homotopy equivalent to $M$ equals the $2$ -nd Betti number (mod $2$ ) of $M$ .

On manifold spines and cyclic presentations of groups

Alberto Cavicchioli; Friedrich Hegenbarth; Dušan Repovš — 1998

Banach Center Publications

This is a survey of results and open problems on compact 3-manifolds which admit spines corresponding to cyclic presentations of groups. We also discuss questions concerning spines of knot manifolds and regular neighborhoods of homotopically PL embedded compacta in 3-manifolds.

Cyclic branched coverings of 2-bridge knots.

Alberto Cavicchioli; Beatrice Ruini; Fulvia Spaggiari — 1999

Revista Matemática Complutense

In this paper we study the connections between cyclic presentations of groups and the fundamental group of cyclic branched coverings of 2-bridge knots. Then we show that the topology of these manifolds (and knots) arises, in a natural way, from the algebraic properties of such presentations.

Surgery on pairs of closed manifolds

Alberto Cavicchioli; Yuri V. Muranov; Fulvia Spaggiari — 2009

Czechoslovak Mathematical Journal

To apply surgery theory to the problem of classifying pairs of closed manifolds, it is necessary to know the subgroup of the group $L P_{*}$ generated by those elements which are realized by normal maps to a pair of closed manifolds. This closely relates to the surgery problem for a closed manifold and to the computation of the assembly map. In this paper we completely determine such subgroups for many cases of Browder-Livesay pairs of closed manifolds. Moreover, very explicit results are obtained in the...