The Maskit embedding
of a surface
is the space of geometrically finite groups on the boundary of
quasifuchsian space for which the “top” end is homeomorphic to
,
while the “bottom” end consists of triply punctured spheres, the remains of
when a
set of pants curves have been pinched. As such representations vary in the character
variety, the conformal structure on the top side varies over the Teichmüller space
.
We investigate
when
is a
twice punctured torus, using the method of pleating rays. Fix a projective measure class
supported on closed
curves on
. The
pleating ray
consists
of those groups in
for which the bending measure of the top component of the convex hull boundary of the associated
–manifold is in
. It is known
that
is a real
–submanifold
of
.
Our main result is a formula for the asymptotic direction of
in
as the
bending measure tends to zero, in terms of natural parameters for the complex
–dimensional
representation space
and the Dehn–Thurston coordinates of the support curves to
relative to the pinched curves on the bottom side. This leads to a method of locating
in
.
