Decomposing four-manifolds up to homotopy type.
Decomposition of modules, forms and simple knots.
Deformation of Maps to Branched Coverings in Dimension Three.
Deloopings of the spaces of long embeddings
The homotopy fiber of the inclusion from the long embedding space to the long immersion space is known to be an iterated based loop space (if the codimension is greater than two). In this paper we deloop the homotopy fiber to obtain the topological Stiefel manifold, combining results of Lashof and of Lees. We also give a delooping of the long embedding space, which can be regarded as a version of Morlet-Burghelea-Lashof's delooping of the diffeomorphism group of the disk relative to the boundary....
Describing toric varieties and their equivariant cohomology
Topologically, compact toric varieties can be constructed as identification spaces: they are quotients of the product of a compact torus and the order complex of the fan. We give a detailed proof of this fact, extend it to the non-compact case and draw several, mostly cohomological conclusions. In particular, we show that the equivariant integral cohomology of a toric variety can be described in terms of piecewise polynomials on the fan if the ordinary integral cohomology is concentrated in even...
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...