Rational Homology 3-Spheres and SL(2,ℂ) Representations
Abstract
We use instanton gauge theory to prove that if Y Y is a closed, orientable 3 3 -manifold such that H 1 ( Y ; Z ) H_{1}(Y;\mathbb {Z}) is nontrivial and either 2 2 -torsion or 3 3 -torsion, and if Y Y is neither # r R P 3 \#^{r} \mathbb {RP}^{3} for some r ≥ 1 r\geq 1 nor ± L ( 3 , 1 ) \pm L(3,1) , then there is an irreducible representation π 1 ( Y ) → SL ( 2 , C ) \pi _{1}(Y) \to \operatorname {SL}(2,\mathbb {C}) . We apply this to show that the Kauffman bracket skein module of a non-prime 3-manifold has nontrivial torsion whenever two of the prime summands are different from R P 3
Fields of Study & Subjects
Geometric and Algebraic Topology
Homotopy and Cohomology in Algebraic Topology
Ophthalmology and Eye Disorders
Publication details
- Journal / source
- Memoirs of the American Mathematical Society
- Volume
- 318
- Issue
- 1618
- Publication date
- 27 February 2026
- Language
- EN