A Note on the Cohomology of Moduli of Rank Two Stable Bundles

In recent years the cohomology ring of the moduli space Ng(2, d) of rank two and odd degree d stable bundles over a Riemann surface M of genus g ≥ 2 has been extensively studied [2], [5], [10], [11]. The subring H(Ng(2, d);Q) Γ of H(Ng(2, d);Q) which is invariant under the induced action of the mapping class group Γ of M has also been much studied and has been shown to play a central role in the ring structure of H(Ng(2, d);Q). In 1991 Zagier [11] began a study of certain relations in the invariant cohomology ring. These are defined recursively in terms of Newstead’s generators α, β, γ [7] by