The virtual Haken conjecture: Experiments and examples.
Three Conjectures of Combinatorial Topology.
Three-manifolds and Kähler groups
We give a simple proof of a result originally due to Dimca and Suciu: a group that is both Kähler and the fundamental group of a closed three-manifold is finite. We also prove that a group that is both the fundamental group of a closed three-manifold and of a non-Kähler compact complex surface is or .
Topological classification of conformal actions on -hyperelliptic Riemann surfaces.
Topological components of spaces of representations.
Topology of arrangements and position of singularities
This work contains an extended version of a course given in Arrangements in Pyrénées. School on hyperplane arrangements and related topics held at Pau (France) in June 2012. In the first part, we recall the computation of the fundamental group of the complement of a line arrangement. In the second part, we deal with characteristic varieties of line arrangements focusing on two aspects: the relationship with the position of the singular points (relative to projective curves of some prescribed degrees)...
Torus knots and Dunwoody manifolds.
Trees of Homotopy Types of Two-Dimensional CW-Complexes
Trees, valuations, and the Bieri-Neumann-Strebel invariant.
Twisted Alexander polynomials and surjectivity of a group homomorphism.
Über Erweiterungen von Z und Z2 * Z2 durch nichteuklidische kristallographische Gruppen.
Über Gruppen von Homöomorphismen Seifertscher Faserräume und flacher Manigfaltigkeiten.
Ultra regular covering space and its automorphism group
In order to classify digital spaces in terms of digital-homotopic theoretical tools, a recent paper by Han (2006b) (see also the works of Boxer and Karaca (2008) as well as Han (2007b)) established the notion of regular covering space from the viewpoint of digital covering theory and studied an automorphism group (or Deck's discrete transformation group) of a digital covering. By using these tools, we can calculate digital fundamental groups of some digital spaces and classify digital covering spaces...
Un nouvel invariant pour les sphères d'homologie de dimension trois
Une obstruction pour scinder une équivalence d’homotopie en dimension
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Which 3-manifold groups are Kähler groups?
The question in the title, first raised by Goldman and Donaldson, was partially answered by Reznikov. We give a complete answer, as follows: if can be realized as both the fundamental group of a closed 3-manifold and of a compact Kähler manifold, then must be finite—and thus belongs to the well-known list of finite subgroups of , acting freely on .
Winding Numbers on Surfaces II. Applications.
Wirtinger presentations for higher dimensional manifold knots obtained from diagrams
A Wirtinger presentation of a knot group is obtained from a diagram of the knot. T. Yajima showed that for a 2-knot or a closed oriented surface embedded in the Euclidean 4-space, a Wirtinger presentation of the knot group is obtained from a diagram in an analogous way. J. S. Carter and M. Saito generalized the method to non-orientable surfaces in 4-space by cutting non-orientable sheets of their diagrams by some arcs. We give a modification to their method so that one does not need to find and...
Zur Faserung von Graphenmannigfaltigkeiten.