Tautological rings for high dimensional manifolds

Abstract

We study tautological rings for high dimensional manifolds, that is, for each smooth manifold $M$ the ring $R^{\ast }(M)$ 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.

16 pages

Cited by in corpus (5)

• A vanishing theorem for tautological classes of aspherical manifolds
• On characteristic classes of exotic manifold bundles
• Rigidity and characteristic classes of smooth bundles with nonpositively curved fibers
• Tautological classes of definite 4-manifolds
• Tautological rings and stabilisation