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Consider the moduli space of parabolic Higgs bundles (E,\Phi) of rank two onCP^1 such that the underlying holomorphic vector bundle for the parabolicvector bundle E is trivial. It is equipped with the natural involution definedby (E,\Phi)\mapsto (E,-\Phi). We study the fixed point locus of thisinvolution. In [GM], this moduli space with involution was identified with themoduli space of hyperpolygons equipped with a certain natural involution. Herewe identify the fixed point locus with the moduli spaces of polygons inMinkowski 3-space. This identification yields information on the connectedcomponents of the fixed point locus.

Polygons in Minkowski three space and parabolic Higgs bundles of rank two on CP^1