We prove that the 3-manifold obtained by gluing the complements of two nontrivial knots in homology 3-sphere instanton -spaces, by a map which identifies meridians with Seifert longitudes, cannot be an instanton -space. This recovers the recent theorem of Lidman–Pinzón-Caicedo–Zentner that the fundamental group of every closed, oriented, toroidal 3-manifold admits a nontrivial -representation, and consequently Zentner’s earlier result that the fundamental group of every closed, oriented -manifold besides the 3-sphere admits a nontrivial -representation.
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