Instanton L-spaces and splicing
Geometric Topology
2022-12-02 v2
Abstract
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, and 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.
Keywords
Cite
@article{arxiv.2103.08087,
title = {Instanton L-spaces and splicing},
author = {John A. Baldwin and Steven Sivek},
journal= {arXiv preprint arXiv:2103.08087},
year = {2022}
}
Comments
18 pages, 8 figures; v2: accepted version