In recently published work Maskit constructs a fundamental domain
Dg for the Teichm\"uller modular group of a closed surface
S of genus g≥2. Maskit's technique is to demand
that a certain set of 2g non-dividing geodesics C2g
on S satisfies certain shortness criteria. This gives
an a priori infinite set of length inequalities that the geodesics
in C2g must satisfy. Maskit shows that this set of
inequalities is finite and that for genus g=2 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
S\C4 for S; 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
