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

2024/06/02 by Shuhei Maruyama, Maruyama, Shuhei
Mathematics · #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2406.00896

openalex publication_date 2024/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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