An explicit relation between knot groups in lens spaces and those in $S^3$

@article{Nozaki2016AnER,
  title={An explicit relation between knot groups in lens spaces and those in \$S^3\$},
  author={Yuta Nozaki},
  journal={arXiv: Geometric Topology},
  year={2016}
}
  • Yuta Nozaki
  • Published 2016
  • Mathematics
  • arXiv: Geometric Topology
For a cyclic covering map $(\Sigma,K) \to (\Sigma',K')$ between two pairs of a 3-manifold and a knot each, we describe the fundamental group $\pi_1(\Sigma \setminus K)$ in terms of $\pi_1(\Sigma' \setminus K')$. As a consequence, we give an alternative proof for the fact that certain knots in $S^3$ cannot be represented as the preimage of any knot in a lens space, which is related to free periods of knots. In our proofs, the subgroup of a group $G$ generated by the commutators and the $p$th… Expand
2 Citations

Tables from this paper

References

SHOWING 1-10 OF 26 REFERENCES
Lift in the 3-sphere of knots and links in lens spaces
  • 7
  • PDF
Noncommutative knot theory.
  • 114
  • PDF
Topology of 3-manifolds and a class of groups
  • 15
  • PDF
Braids and Permutations
  • 38
  • PDF
ON GROUPS GENERATED BY THE SQUARES
  • 2
  • PDF
Homology and derived p-series of groups
  • 10
A new criterion for knots with free periods
  • 7
  • Highly Influential
  • PDF
A Course in the Theory of Groups
  • 2,988
...
1
2
3
...