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We investigate the Lawson genus $2$ surface by methods from integrable systemtheory. We prove that the associated family of flat connections comes from afamily of flat connections on a $4-$punctured sphere. We describe thesymmetries of the holonomy and show that it is already determined by theholonomy around one of the punctures. We show the existence of a meromorphicDPW potential for the Lawson surface which is globally defined on the surface.We determine this potential explicitly up to two unknown functions dependingonly on the spectral parameter.

Lawson's genus two minimal surface and meromorphic connections