Abstract

Let F : M³↪R⁵ be an embedding of an (oriented) Z₂-homology 3-sphere M³ in R⁵. Then F bounds an embedding of an oriented manifold W⁴ in R⁵. It is well known that the signature σ(W⁴) of W⁴ is equal to the μ-invariant of M³ modulo 16. In this paper we prove that σ(W⁴) itself completely determines the regular homotopy class of F.

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