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Tautological rings for high dimensional manifolds (1511.06445v1)
Published 19 Nov 2015 in math.AT
Abstract: We study tautological rings for high dimensional manifolds, that is, for each smooth manifold $M$ the ring $R*(M)$ of those of characteristic classes of smooth fibre bundles with fibre $M$ which is generated by generalised Miller--Morita--Mumford classes. We completely describe these rings modulo nilpotent elements, when $M$ is a connected sum of copies of $Sn \times Sn$ for $n$ odd.