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Tautological rings of fibrations

Nils Prigge
Algebraic & Geometric Topology 26 (2026) 1565–1584
DOI: 10.2140/agt.2026.26.1565
Abstract

We study the analogue of tautological rings of fibre bundles in the context of fibrations with Poincaré 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.

Keywords
characteristic classes, fibrations, tautological ring, rational homotopy theory
Mathematical Subject Classification
Primary: 55R40
References
Publication
Received: 11 October 2024
Revised: 9 April 2025
Accepted: 25 April 2025
Published: 25 April 2026
Authors
Nils Prigge
Matematiska Institutionen
Stockholm University
Stockholm
Sweden
© 2026 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY).

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