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Geometry of the complex of curves I: Hyperbolicity

โœ Scribed by Howard A. Masur; Yair N. Minsky


Publisher
Springer-Verlag
Year
1999
Tongue
English
Weight
318 KB
Volume
138
Category
Article
ISSN
0020-9910

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We show that plane hyperbolic geometry, expressed in terms of points and the ternary relation of collinearity alone, cannot be expressed by means of axioms of complexity at most โˆ€โˆƒโˆ€, but that there is an axiom system, all of whose axioms are โˆ€โˆƒโˆ€โˆƒ sentences. This remains true for Klingenberg's genera