Gaps of saddle connection directions for some branched covers of tori
| Autor: | Anthony Sanchez |
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| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Applied Mathematics General Mathematics 010102 general mathematics Connection (vector bundle) Geometric Topology (math.GT) Dynamical Systems (math.DS) 16. Peace & justice Translation (geometry) 01 natural sciences Moduli space Mathematics - Geometric Topology Horocycle Transversal (combinatorics) 0103 physical sciences Translation surface FOS: Mathematics 37A17 (Primary) 37D40 32G15 (Secondary) 010307 mathematical physics Mathematics - Dynamical Systems 0101 mathematics Distribution (differential geometry) Saddle Mathematics |
| DOI: | 10.48550/arxiv.2004.04182 |
| Popis: | We compute the gap distribution of directions of saddle connections for two classes of translation surfaces. One class will be the translation surfaces arising from gluing two identical tori along a slit. These yield the first explicit computations of gap distributions for non-lattice translation surfaces. We show that this distribution has support at 0 and quadratic tail decay. We also construct examples of translation surfaces in any genus $d>1$ that have the same gap distribution as the gap distribution of two identical tori glued along a slit. The second class we consider are twice-marked tori and saddle connections between distinct marked points. These results can be interpreted as the gap distribution of slopes of affine lattices. We obtain our results by translating the question of gap distributions to a dynamical question of return times to a transversal under the horocycle flow on an appropriate moduli space. 56 pages, 7 figures, made some contributions clearer such as the results on the transversal and affine lattices |
| Databáze: | OpenAIRE |
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