On the cohomology of the classifying spaces of SO(n)-gauge groups over S²

2023/04/18 by Yuki Minowa, Minowa, Yuki
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2304.08702

openalex publication_date 2023/04/18 · openalex created_date 2023/04/22 · openalex updated_date 2026/07/28

Abstract

Let G_α(X, G) be the G-gauge group over a space X corresponding to a map α\colon X → BG. We compute the integral cohomology of BG₁(S², SO(n)) for n = 3,4. We also show that the homology of BG₁(S², SO(n)) is torsion free if and only if n≤ 4. As an application, we classify the homotopy types of SO(n)-gauge groups over a Riemann surface for n≤ 4.

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