# Integer homology \$3\$-spheres admit irreducible representations in \$\operatorname{SL}(2,\mathbb{C})\$

```@article{Zentner2016IntegerH,
title={Integer homology \\$3\\$-spheres admit irreducible representations in \\$\operatorname\{SL\}(2,\mathbb\{C\})\\$},
author={R. Zentner},
journal={Duke Mathematical Journal},
year={2016},
volume={167},
pages={1643-1712}
}```
• R. Zentner
• Published 2016
• Mathematics
• Duke Mathematical Journal
• We prove that the fundamental group of any integer homology 3-sphere different from the 3-sphere admits irreducible representations of its fundamental group in SL(2,C). For hyperbolic integer homology spheres this comes with the definition, and for Seifert fibered integer homology spheres this is well known. We prove that the splicing of any two non-trivial knots in the 3-sphere admits an irreducible SU(2)-representation. By work of Boileau, Rubinstein, and Wang, the general case follows. Using… CONTINUE READING
19 Citations

#### Figures from this paper.

On the treewidth of triangulated 3-manifolds
• Mathematics, Computer Science
• Symposium on Computational Geometry
• 2018
• 10
• PDF
Embeddability in R3 is NP-hard
• Mathematics, Computer Science
• J. ACM
• 2020
• 11
• PDF
On the hardness of finding normal surfaces
• Mathematics, Computer Science
• ArXiv
• 2019