ISSN:
1436-5081
Keywords:
53A35
;
57M50
;
11J06
;
geodesic
;
punctured torus
;
Markoff spectrum, diophantine approximation
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We classify the free homotopy classes of closed curves with minimal self intersection number two on a once punctured torus,T, up to homeomorphism. Of these, there are six primitive classes and two imprimitive. The classification leads to the topological result that, up to homeomorphism, there is a unique curve in each class realizing the minimum self intersection number. The classification yields a complete classification of geodesics on hyperbolicT which have self intersection number two. We also derive new results on the Markoff spectrum of diophantine approximation; in particular, exactly three of the imprimitive classes correspond to families of Markoff values below Hall's ray.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01317313
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