# Instanton L-spaces and splicing

Tuesday, April 27, 2021 10:00 AM

John A. Baldwin (Boston College)

We prove that the 3-manifold obtained by gluing the complements of two nontrivial knots in homology 3-sphere instanton L-spaces, by a map which identifies meridians with Seifert longitudes, cannot be an instanton L-space. This recovers the recent theorem of Lidman–Pinzon-Caicedo–Zentner that the fundamental group of every closed, oriented, toroidal 3-manifold admits a nontrivial SU(2)-representation, and consequently Zentner’s earlier result that the fundamental group of every closed, oriented 3-manifold besides the 3-sphere admits a nontrivial SL(2, C)-representation. This is joint work with Steven Sivek.