Hyperbolicity via Geodesic Stability
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2015
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| _version_ | 1866909993512468480 |
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| author | Fink, Elisabeth |
| author_facet | Fink, Elisabeth |
| contents | A geodesic $g$ is Morse, for every $L \geq 1, A \geq 0$ there exists a $C=C_g(L,A)$ such that any $(L,A)$-quasi-geodesic connecting two points on $g$ stays $C$-close to $g$. The Morse lemma implies that in a hyperbolic space every geodesic is Morse. Here we prove the converse: If a homogeneous proper geodesic space is such that for every geodesic $g$ and every $L\geq 1, A \geq 0$ there exists a constant $C=C_g(L,A)$ such that any $(L,A)$-quasi-geodesic between any two points on $g$ stays $C$-close, then the space is hyperbolic. This applies in particular to infinite groups in which all geodesics are Morse. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1504_06863 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | Hyperbolicity via Geodesic Stability Fink, Elisabeth Metric Geometry Group Theory Geometric Topology A geodesic $g$ is Morse, for every $L \geq 1, A \geq 0$ there exists a $C=C_g(L,A)$ such that any $(L,A)$-quasi-geodesic connecting two points on $g$ stays $C$-close to $g$. The Morse lemma implies that in a hyperbolic space every geodesic is Morse. Here we prove the converse: If a homogeneous proper geodesic space is such that for every geodesic $g$ and every $L\geq 1, A \geq 0$ there exists a constant $C=C_g(L,A)$ such that any $(L,A)$-quasi-geodesic between any two points on $g$ stays $C$-close, then the space is hyperbolic. This applies in particular to infinite groups in which all geodesics are Morse. |
| title | Hyperbolicity via Geodesic Stability |
| topic | Metric Geometry Group Theory Geometric Topology |
| url | https://arxiv.org/abs/1504.06863 |