Die Unterscheidung von Homotopietyp und einfachem Homotopietyp bei zweidimensionalen Komplexen.
Die Werte der Franz-Reidemeister-Torsion bei torsionsberandenden Mannigfaltigkeiten.
Discrete Morse inequalities on infinite graphs.
Discrete Morse theory and graph braid groups.
Disjonction de sous-variétés et application au croisement des anses
Dotted links, Heegaard diagrams, and colored graphs for PL 4-manifolds.
The present paper is devoted to establish a connection between the 4-manifold representation method by dotted framed links (or -in the closed case- by Heegaard diagrams) and the so called crystallization theory, which visualizes general PL-manifolds by means of edge-colored graphs.In particular, it is possible to obtain a crystallization of a closed 4-manifold M4 starting from a Heegaard diagram (#m(S1 x S2),ω) and the algorithmicity of the whole process depends on the effective possibility of recognizing...
Double suspension d'une sphère d'homologie
Dynamical zeta functions, congruences in Nielsen theory and Reidemeister torsion
In this paper we prove trace formulas for the Reidemeister numbers of group endomorphisms and the rationality of the Reidemeister zeta function in the following cases: the group is finitely generated and the endomorphism is eventually commutative; the group is finite; the group is a direct sum of a finite group and a finitely generated free Abelian group; the group is finitely generated, nilpotent and torsion free. We connect the Reidemeister zeta function of an endomorphism of a direct sum of a...
Effectiveness - non effectiveness in semialgebraic and PL geometry.
Ein Endlichkeitssatz für Klassenzahlen invarianter Formen.
Ein kombinatorisches Analogon zum Satz von Gauss-Bonnet.
El teorema del punto fijo sin homología: un enfoque combinatorio.
Elementary moves for higher dimensional knots
For smooth knottings of compact (not necessarily orientable) n-dimensional manifolds in (or ), we generalize the notion of knot moves to higher dimensions. This reproves and generalizes the Reidemeister moves of classical knot theory. We show that for any dimension there is a finite set of elementary isotopies, called moves, so that any isotopy is equivalent to a finite sequence of these moves.
Embedding, compression and fiberwise homotopy theory.
Embedding Finite Covering Spaces into Trivial Bundles.
Embedding products of graphs into Euclidean spaces
For any collection of graphs we find the minimal dimension d such that the product is embeddable into (see Theorem 1 below). In particular, we prove that (K₅)ⁿ and are not embeddable into , where K₅ and are the Kuratowski graphs. This is a solution of a problem of Menger from 1929. The idea of the proof is a reduction to a problem from so-called Ramsey link theory: we show that any embedding , where O is a vertex of (K₅)ⁿ, has a pair of linked (n-1)-spheres.
Embedding proper homotopy types
We show that the proper homotopy type of any properly c-connected locally finite n-dimensional CW-complex is represented by a closed polyhedron in (Theorem I). The case n - c ≥ 3 is a special case of a general proper homotopy embedding theorem (Theorem II). For n - c ≤ 2 we need some basic properties of “proper” algebraic topology which are summarized in Appendices A and B. The results of this paper are the proper analogues of classical results by Stallings [17] and Wall [20] for finite CW-complexes;...
Embeddings and imnmersions of branched covering spaces.
Ends of Maps, II.
Enlacements d’intervalles et torsion de Whitehead
Soit un enlacement de intervalles dans d’extérieur et soit . On utilise la propriété de la paire d’être -acyclique pour certaines représentation de l’anneau du groupe fondamental de dans un anneau pour construire des invariants de torsion à valeurs dans le groupe . Un cas particulier est le polynôme d’Alexander en variables quand est l’anneau des fractions rationnelles avec et est simplement l’abélianisation.