Let $B$ be $k$-dimensional PL-ball and let $M$ be a connected $n$-dimensional PL-manifold, let's say without boundary. Furthermore let $f,g\colon B\to M$ be two PL-embeddings. If $k=n$, then the disc theorem (see Theorem 3.34 in Rourke-Sanderson) says that, after possibly composing $f$ by a reflection, $f$ and $g$ are ambiently isotopic.

Now assume that $k<n$. Is it true that $f$ and $g$ are necessarily ambiently isotopic?

If we work in the smooth category, then the answer would be yes. But I am very unsure about the PL-category.

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