Abstract
We explicitly compute the outer automorphism group Out π1 M of the fundamental group of the Hantzsche — Wendt manifoldM. It is an extension 1→(ℤ2)3→Outπ1 M→S 3⊕ℤ2→1, but not the semidirect product (ℤ2)3⋉(S 3⊕ℤ2) as claimed in [3] (see also [4]). As a consequence, we get a quick algebraic computation of the symmetry groups of the Borromean rings and the figure-8-knot.
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Zimmermann, B. On the Hantzsche-Wendt manifold. Monatshefte für Mathematik 110, 321–327 (1990). https://doi.org/10.1007/BF01301685
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DOI: https://doi.org/10.1007/BF01301685