Character varieties and knot symmetries. (English) Zbl 1422.57041
Summary: Those are notes of the mini-course given in the school Winter Braids VII, held in Caen from February 27th to March 2nd 2017. They overview the variety of representations and characters of a three-manifold in \(\operatorname{SL}_2 \mathbb{C}\), putting emphasis on explicit computations. The notes also discuss the canonical component of a hyperbolic knot, and a recent joint work with L. Paoluzzi [Math. Proc. Camb. Philos. Soc. 165, No. 2, 193–208 (2018; Zbl 1400.57016)], on the invariant components of the variety of characters for knot symmetries.
MSC:
| 57M27 | Invariants of knots and \(3\)-manifolds (MSC2010) |
| 57-02 | Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes |
Keywords:
mini-course; representations; characters; three-manifolds; computations; \(\mathrm{SL}_2\mathbb C\)Citations:
Zbl 1400.57016References:
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