McDuff's secondary class and the Euler class of foliated sphere bundles

Shuhei Maruyama

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arXiv · 2406.00896

McDuff's secondary class and the Euler class of foliated sphere bundles

Shuhei Maruyama

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Abstract

Tsuboi proved that the Calabi invariant of the closed disk transgresses to the Euler class of foliated circle bundles and suggested looking for its higher-dimensional analog. In this paper, we construct a cohomology class of the group of volume-preserving diffeomorphisms of a real-cohomologically acyclic manifold with sphere boundary, which is closely related to McDuff's secondary class, and prove that this cohomology class transgresses to the Euler class of foliated sphere bundles.

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Shuhei Maruyama. 2024-06-02. McDuff's secondary class and the Euler class of foliated sphere bundles. https://arxiv.org/abs/2406.00896

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