Proof of Kuiper's theorem (that U(ℋ) is contractible in the norm topology):
On microbundles:
N. H. Kuiper and R. K. Lashof, Microbundles and Bundles I. Elementary Theory, Invent. Math., 1, (1966), 1 – 17.
N. H. Kuiper and R. K. Lashof, Microbundles and Bundles II. Semisimplicial Theory, Invent. Math., 1, (1966), 243 – 259.
The Arnold-Kuiper-Massey theorem:
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