Instanton L-spaces and splicing
File(s)
Published version
Author(s)
Baldwin, John A
Sivek, Steven
Type
Journal Article
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, Pinzón-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.
Date Issued
2022-11-01
Date Acceptance
2022-04-23
Citation
Annales Henri Lebesgue, 2022, 5, pp.1213-1233
ISSN
2644-9463
Start Page
1213
End Page
1233
Journal / Book Title
Annales Henri Lebesgue
Volume
5
Copyright Statement
© 2022 Centre Mersenne, Annales Henri Lebesgue, and the authors. Published under license CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/)
License URL
Subjects
math.GT
math.GT
Publication Status
Published