  Consider the moduli space of parabolic Higgs bundles (E,\Phi) of rank two on
CP^1 such that the underlying holomorphic vector bundle for the parabolic
vector bundle E is trivial. It is equipped with the natural involution defined
by (E,\Phi)\mapsto (E,-\Phi). We study the fixed point locus of this
involution. In [GM], this moduli space with involution was identified with the
moduli space of hyperpolygons equipped with a certain natural involution. Here
we identify the fixed point locus with the moduli spaces of polygons in
Minkowski 3-space. This identification yields information on the connected
components of the fixed point locus.
