A note on invariants of foliated 3-sphere bundles

2024/09/10 by Nils Prigge, Prigge, Nils
Mathematics · #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2409.06408

openalex publication_date 2024/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we prove that H^*(BSO(4);ℚ) injects into the group cohomology of Diff⁺(S³) with rational coefficients. The proof is based on an idea of Nariman who proved that the monomials in the Euler and Pontrjagin classes are nontrivial in H^*(BDiff₊^δ(S^2n-1);ℚ).

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