A class of knots with simple SU(2)-representations

@article{Zentner2017ACO,
  title={A class of knots with simple SU(2)-representations},
  author={Raphael Zentner},
  journal={Selecta Mathematica},
  year={2017},
  volume={23},
  pages={2219-2242}
}
We call a knot in the 3-sphere SU(2)-simple if all representations of the fundamental group of its complement which map a meridian to a trace-free element in SU(2) are binary dihedral. This is a generalization of being a 2-bridge knot. Pretzel knots with bridge number $${\ge }3$$≥3 are not SU(2)-simple. We provide an infinite family of knots K with bridge number $${\ge }3$$≥3 which are SU(2)-simple. One expects the instanton knot Floer homology $$I^\natural (K)$$I♮(K) of a SU(2)-simple knot to… Expand
9 Citations
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