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In recently published work Maskit constructs a fundamental domain
for the Teichmüller modular group of a closed surface
of genus
.
Maskit’s technique is to demand that a certain set of
non-dividing
geodesics
on
satisfies
certain shortness criteria. This gives an a priori infinite set of length inequalities that the
geodesics in
must satisfy. Maskit shows that this set of inequalities is finite and that for genus
there are
at most 45. In this paper we improve this number to 27. Each of these inequalities:
compares distances between Weierstrass points in the fundamental domain
for
; and
is realised (as an equality) on one or other of two special surfaces.
Keywords
fundamental domain, non-dividing geodesic, Teichmüller
modular group, hyperelliptic involution, Weierstrass point