Invariants of real vector bundles

2023/10/08 by Hu, Jiahao
#Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2310.05061

Abstract

For a compact smooth manifold with corners (or finite CW-complex) X, we can prescribe a finite set of spin or spin^h manifolds (possibly with boundary) mapping into it so that every real vector bundle over X is determined, up to stable equivalence, by the Dirac indices of the real vector bundle when pulled-back onto those prescribed spin or spin^h manifolds.

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