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MR1254861 (95b:57015) 57N10 (57M20 57Q35)
Li, Zhong Mou Every $3$-manifold with boundary embeds in ${\rm Triod}\times {\rm Triod}\times I$. Proc. Amer. Math. Soc. 122 (1994), no. 2, 575–579.
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