Rational Homology 3-spheres and $\mathrm{SL}(2,\mathbb{C})$ Representations

Sudipta Ghosh, University of Notre Dame, Indiana, Steven Sivek, Imperial College London, United Kingdom, and Raphael Zentner, Durham University, United Kingdom

1. Introduction 2. Instanton Floer homology 3. Closed curves in the pillowcase 4. Pinching and the twisted $I$-bundle over the Klein bottle 5. Splicing knots in manifolds with $2$-torsion homology 6. Gluing complements of knots in sums of $\mathbb {RP}^{3}$ 7. Toroidal manifolds as unions of knot complements 8. Proof of Theorem 9. From $\mathbb {Z}/p\mathbb {Z}$ to $p$-torsion homology 10. Manifolds with $3$-torsion homology A. The surgery exact triangle in irreducible instanton homology