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arXiv · 1511.06445

Tautological rings for high dimensional manifolds

Soren Galatius·Ilya Grigoriev·Oscar Randal-Williams
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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 $S^n \times S^n$ for $n$ odd.

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Soren Galatius, Ilya Grigoriev, Oscar Randal-Williams. 2015-11-19. Tautological rings for high dimensional manifolds. https://doi.org/10.1112/s0010437x16008332

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