Tautological rings for high-dimensional manifolds

We study tautological rings for high-dimensional manifolds, that is, for each smooth manifold $M$ the ring $R^{\ast }(M)$ of those 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 $S^{n}\times S^{n}$ for $n$ odd.

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Tautological rings for high-dimensional manifolds

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Article contents

Tautological rings for high-dimensional manifolds

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MSC classification

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