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arxiv: 1905.02676 · v2 · submitted 2019-05-07 · 🧮 math.AT

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Tautological Rings of Fibrations

Nils Prigge
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classification 🧮 math.AT
keywords fibreringtautologicaleulerfibrationsringsspheresanalogue
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We study the analogue of tautological rings of fibre bundles in the context of fibrations with Poincar\' e fibre, i.e. the ring obtained by fibre integrating powers of the fibrewise Euler class. We discuss how to compute the Euler ring with tools from rational homotopy theory and completely determine the tautological ring for even spheres, complex projective spaces and some products of odd spheres.

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  1. Rational characteristic classes of bundles with fibre a product of spheres

    math.AT 2026-04 unverdicted novelty 7.0

    The rational characteristic class ring for oriented S^n x S^n-fibrations injects into smooth bundle cohomology, producing non-trivial classes in all degrees detected by bundles from cyclic subgroups of a finite-index ...