Real spin bundles over ℂP³ and a new Euclidean embedding of ℝP⁷

2025/11/15 by Dominik Gdesz, Gdesz, Dominik
Mathematics · #55R50 (Secondary) #57R40 (Primary) 55R25 #Advanced Operator Algebra Research #Algebraic Topology (math.AT) #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2511.12172

openalex publication_date 2025/11/15 · openalex created_date 2025/11/19 · openalex updated_date 2026/07/28

Abstract

We generalize the α-invariant introduced by Atiyah and Rees to an invariant of real spin bundles and use it to classify real bundles over ℂP³ admitting spin structure. We apply this result to show that ℝP⁷ can be smoothly embedded in ℝP¹¹.

Citations

• Einlagerung von Mannigfaltigkeiten in euklidische R�ume

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