Length spectra of flat metrics coming from $q$-differentials
| Autor: | Marissa Loving |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Spectrum (functional analysis)
Mathematical analysis Geometric Topology (math.GT) 16. Peace & justice Spectral line Mathematics - Geometric Topology Integer Cone (topology) Simple (abstract algebra) Metric (mathematics) Euclidean geometry FOS: Mathematics 57M50 58J50 Discrete Mathematics and Combinatorics Geometry and Topology Quadratic differential Mathematics |
| Zdroj: | Groups, Geometry, and Dynamics. 14:1223-1240 |
| ISSN: | 1661-7207 |
| DOI: | 10.4171/ggd/578 |
| Popis: | When geometric structures on surfaces are determined by the lengths of curves, it is natural to ask: which curves' lengths do we really need to know? It is a result of Duchin--Leininger--Rafi that any flat metric induced by a unit-norm quadratic differential is determined by its marked simple length spectrum. We generalize the notion of simple curves to that of q-simple curves, for any positive integer q, and show that the lengths of q-simple curves suffice to determine a non-positively curved Euclidean cone metric induced by a q-differential. An error in the proof of Proposition 3.2 (which is split between the proofs of Lemma 3.1 and 3.2) in the case that q is even has been corrected. The changes involve a slight modification of Definition 3.1 and a short paragraph at the end of each of the proofs of Lemmas 3.1 and 3.2 |
| Databáze: | OpenAIRE |
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