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- W4285024444 abstract "We sketch a geometric proof of the classical theorem of Atiyah, Bott, and Shapiro cite{ABS} which relates Clifford modules to vector bundles over spheres. Every module of the Clifford algebra $Cl_k$ defines a particular vector bundle over $S^{k+1}$, a generalized Hopf bundle, and the theorem asserts that this correspondence between $Cl_k$-modules and stable vector bundles over $S^{k+1}$ is an isomorphism modulo $Cl_{k+1}$-modules. We prove this theorem directly, based on explicit deformations as in Milnor's book on Morse theory cite{M}, and without referring to the Bott periodicity theorem as in cite{ABS}." @default.
- W4285024444 created "2022-07-12" @default.
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- W4285024444 date "2016-10-14" @default.
- W4285024444 modified "2023-09-26" @default.
- W4285024444 title "Bott Periodicity, Submanifolds, and Vector Bundles" @default.
- W4285024444 doi "https://doi.org/10.48550/arxiv.1610.04385" @default.
- W4285024444 hasPublicationYear "2016" @default.
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