J. Aust. Math. Soc.
74 (2003), 43-60|
Parametrizing simple closed geodesy on
| We exhibit a canonical geometric pairing of the
simple closed curves of the degree three cover of
the modular surface,
the proper single self-intersecting
geodesics of Crisp and Moran. This leads to a
pairing of fundamental domains for
with Markoff triples.|
The routes of the simple
closed geodesics are directly related to the
above. We give two parametrizations of these.
Combining with work of Cohn, we achieve a
listing of all simple closed geodesics of length
within any bounded interval. Our method is
direct, avoiding the determination of geodesic
lengths below the chosen lower bound.
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