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We study the singular cohomology of the moduli space of rank 2 parabolicbundles on a Riemann surface where the weights are all 1/4. We give a formula,based on work of Boden, for the Poincar\'e polynomial of this moduli space ingeneral, and deduce a complete set of relations in the cohomology ring for thecase when the genus is zero. These relations are recursive in the number ofparabolic points (which must be odd), and are analogous to the relationsappearing in the cohomology ring for the non-parabolic story, which arerecursive in the genus. Our methods use techniques from a paper of Weitsman toreduce to a linear algebra problem, which we then solve using the theory oforthogonal polynomials and a continued fraction expansion for the generatingfunction of the Euler numbers.

Recursive relations in the cohomology rings of moduli spaces of rank 2 parabolic bundles on the Riemann sphere