Tiling the Torus and Other Space Forms.
Tiling with L's and squares.
Tiling with smooth and rotund tiles
Tilings and isoperimetrical shapes I: Square lattice
Tilings and isoperimetrical shapes. II. Hexagonal lattice
Tilings associated with beta-numeration and substitutions.
Tilings associated with non-Pisot matrices
Suppose has a 2-dimensional expanding subspace , satisfies a regularity condition, called “good star”, and has , where is an oriented compound of . A morphism of the free group on is called a non-abelianization of if it has structure matrix . We show that there is a tiling substitution whose “boundary substitution” is a non-abelianization of . Such a tiling substitution leads to a self-affine tiling of with as its expansion. In the last section we find conditions on so...
Tilings in topological spaces.
Tilings of convex polygons
Call a polygon rational if every pair of side lengths has rational ratio. We show that a convex polygon can be tiled with rational polygons if and only if it is itself rational. Furthermore we give a necessary condition for an arbitrary polygon to be tileable with rational polygons: we associate to any polygon a quadratic form , which must be positive semidefinite if is tileable with rational polygons.The above results also hold replacing the rationality condition with the following: a polygon...
Tilings of the Square with Similar Rectangles.
Tilings with the neighborhood property.
Topological criteria for -formal arrangements.
Topological Order Complexes and Resolutions of Discriminant Sets
Topological order complexes and resolutions of discriminant sets.
Topological proper separation theorems
Topological Representation of Dual Pairs of Oriented Matroids.
Topological Structure of Non-separable Sigma-locally Compact Convex Sets
Topologies faciales dans les convexes compacts. Calcul fonctionnel et décomposition spectrale dans le centre d’un espace
Cet article étudie, sur l’ensemble des points extrémaux d’un convexe compact , des topologies faciales dont les fermés sont les traces de faces “parallélisables” (il existe une plus grande face disjointe de , et tout de s’écrit , avec unique). Les topologies faciales uniformisables sont en bijection avec les sous-espaces réticulés fermés et contenant 1 de l’espace des fonctions affines continues sur . Ceci redonne des résultats classiques sur les simplexes, et permet une étude...
Topology and geometry of nontrivial rank-one convex hulls for two-by-two matrices
Continuing earlier work by Székelyhidi, we describe the topological and geometric structure of so-called T4-configurations which are the most prominent examples of nontrivial rank-one convex hulls. It turns out that the structure of T4-configurations in is very rich; in particular, their collection is open as a subset of . Moreover a previously purely algebraic criterion is given a geometric interpretation. As a consequence, we sketch an improved algorithm to detect T4-configurations. ...
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)...