#### Volume 11, issue 5 (2011)

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Representation spaces of pretzel knots

### Raphael Zentner

Algebraic & Geometric Topology 11 (2011) 2941–2970
##### Abstract

We study the representation spaces $R\left(K;i\right)$ appearing in Kronheimer and Mrowka’s instanton knot Floer homologies for a class of pretzel knots. In particular, for pretzel knots $P\left(p,q,r\right)$ with $p,q,r$ pairwise coprime, these appear to be nondegenerate and comprise representations in $SU\left(2\right)$ that are not binary dihedral.

##### Keywords
knot, pretzel knot, representation space, $\mathrm{SU}(2)$, instanton knot Floer homology
##### Mathematical Subject Classification 2000
Primary: 57M25, 57M27
Secondary: 57R58