The accessibility of finitely presented groups.
The edge-minimal polyhedral maps of Euler characteristic .
The Homotopoy Type of Four-Dimensional Knot Complements.
The Homotype Type of a Combinatorially Aspherical Presentation.
The integral homology of SL2 and PSL2 of euclidean imaginary quadratic integers.
The reduction of quantum invariants of 4-thickenings
We study the sensibility of an invariant of 2-dimensional CW complexes in the case when it comes as a reduction (through a change of ring) of a modular invariant of 4-dimensional thickenings of such complexes: it is shown that if the Euler characteristic of the 2-complex is greater than or equal to 1, its invariant depends only on homology. To see what is happening when the Euler characteristic is smaller than 1, we use ideas of Kerler and construct, from any tortile category, an invariant of 4-thickenings...
The surjectivity problem for one-generator, one-relator extensions of torsion-free groups.
Three Conjectures of Combinatorial Topology.
Tight Polyhedral Klein Bottles, Projective Planes, and Möbius Bands.
Tiling systems and homology of lattices in tree products.
Trees of Homotopy Types of Two-Dimensional CW-Complexes