Representation spaces of pretzel knots

@article{Zentner2011RepresentationSO,
  title={Representation spaces of pretzel knots},
  author={Raphael Zentner},
  journal={Algebraic & Geometric Topology},
  year={2011},
  volume={11},
  pages={2941-2970}
}
We study the representation spaces $R(K;\bf{i})$ as appearing in Kronheimer and Mrowka's framed instanton knot Floer homology, for a class of pretzel knots. In particular, for pretzel knots $P(p,q,r)$ with $p, q, r$ pairwise coprime, these appear to be non-degenerate and comprise representations in SU(2) that are not binary dihedral. 
8 Citations

Figures and Tables from this paper

Traceless SU(2) representations of 2-stranded tangles
  • 8
  • PDF
A class of knots with simple SU(2)-representations
  • 9
  • PDF
LINK HOMOLOGY AND EQUIVARIANT GAUGE THEORY
  • 7
  • PDF
The pillowcase and perturbations of traceless representations of knot groups
  • 31
  • Highly Influenced
  • PDF
On spectral sequences from Khovanov homology
  • 9
  • PDF
Tracefree ${\rm SL}(2,\mathbb{C})$-representations of Montesinos links
  • 1
  • PDF

References

SHOWING 1-10 OF 25 REFERENCES
Deformations of dihedral representations
  • 20
  • PDF
Representations of knot groups in SU(2)
  • 129
  • Highly Influential
  • PDF
Deforming abelian SU(2)-representations of knot groups
  • 40
  • PDF
Khovanov homology is an unknot-detector
  • 200
  • PDF
Knot homology groups from instantons
  • 97
  • Highly Influential
  • PDF
A knot invariant via representation spaces
  • 76
  • PDF
Instanton Homology of Seifert Fibred Homology Three Spheres
  • 194
  • PDF
Khovanov homology of alternating links and SU(2) representations of the link group
  • 5
  • PDF
A categorification of the Jones polynomial
  • 720
  • PDF
...
1
2
3
...