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arXiv · 2409.16557

Complex K-theory of 4-complexes

Jonathan Rosenberg
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Abstract

This short note summarizes a number of facts about the ring $K^0(X)$ for $X$ a $4$-dimensional CW-complex. Unusual features of this dimension are that every complex vector bundle is determined up to stable isomorphism by its Chern classes, that every even cohomology class arises as a Chern class of a vector bundle, and that $K^0(X)$ is completely determined as a ring by knowledge of the even-dimensional cohomology ring $H^{\text{even}}(X; \mathbb Z)$. (All of these fail in high dimensions.)

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Jonathan Rosenberg. 2024-09-25. Complex K-theory of 4-complexes. https://arxiv.org/abs/2409.16557

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