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Let  be a compact Riemann surface together with a finite set of marked points. We use Morse theoretic techniques to compute the Betti numbers of the parabolic (2,1)-Higgs bundles moduli spaces over . We give examples for one marked point showing that the Poincaré polynomials depend on the system of weights of the parabolic bundle.

Betti Numbers of parabolic U(2,1)-Higgs bundles moduli spaces