Similarity structures on the torus and the Klein bottle via triangulations
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Stefano Francaviglia
Abstract
In this paper we study the possibility of defining a similarity structure on the torus and the Klein bottle using the combinatorial data of a triangulation. Given a choice of moduli for the triangles of a triangulation of a surface, the problem is to decide whether such moduli are compatible with a global similarity structure on the surface.
We study this problem under two dierent viewpoints. From one side we look at the combinatorial data of triangulations, and we develop an algorithmic method, which allows us to reduce the general problem to a simpler one, which is easily solved. From the other side we study the problem more algebraically, looking at the properties of the holonomy, and we give a complete characterization of the choices of moduli defining global similarity structures on the torus (or on the Klein bottle).
© Walter de Gruyter
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- On the surjectivity of the canonical Gaussian map for multiple coverings
- A classification of 4-dimensional elation Laguerre planes of group dimension 10
- Completely regular ovals
- Symmetry and the farthest point mapping on convex surfaces
- Certain Roman and flock generalized quadrangles have nonisomorphic elation groups
- Similarity structures on the torus and the Klein bottle via triangulations
- On Euclidean designs
- Carnot spaces and the k-stein condition
- Simplicity of the universal quotient bundle restricted to congruences of lines in ℙ3
- Entropy of the geodesic flow for metric spaces and Bruhat–Tits buildings
Artikel in diesem Heft
- On the surjectivity of the canonical Gaussian map for multiple coverings
- A classification of 4-dimensional elation Laguerre planes of group dimension 10
- Completely regular ovals
- Symmetry and the farthest point mapping on convex surfaces
- Certain Roman and flock generalized quadrangles have nonisomorphic elation groups
- Similarity structures on the torus and the Klein bottle via triangulations
- On Euclidean designs
- Carnot spaces and the k-stein condition
- Simplicity of the universal quotient bundle restricted to congruences of lines in ℙ3
- Entropy of the geodesic flow for metric spaces and Bruhat–Tits buildings
