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We study piecewise linear co-dimension two embeddings of closed orientedmanifolds in Euclidean space, and show that any such embedding can always beisotoped to be a closed braid as long as the ambient dimension is at most five,extending results of Alexander (in ambient dimension three), and Viro andindependently Kamada (in ambient dimension four). We also show an analogousresult for higher co-dimension embeddings.

Piecewise linear generalized Alexander's theorem in dimension at most 5