• Corpus ID: 252532120

The Ma-Qiu index and the Nakanishi index for a fibered knot are equal, and $\omega$-solvability

@inproceedings{Kadokami2022TheMI,
  title={The Ma-Qiu index and the Nakanishi index for a fibered knot are equal, and \$\omega\$-solvability},
  author={Teruhisa Kadokami},
  year={2022}
}
For a knot K in S 3 , let G ( K ) be the knot group of K , a ( K ) the Ma-Qiu index (the MQ index, for short), which is the minimal number of normal generators of the commutator subgroup of G ( K ), and m ( K ) the Nakanishi index of K , which is the minimal number of generators of the Alexander module of K . We generalize the notions for a pair of a group G and its normal sugroup N , and we denote them by a ( G, N ) and m ( G, N ) respectively. Then it is easy to see m ( G, N ) ≤ a ( G, N ) in… 

References

SHOWING 1-10 OF 11 REFERENCES

An integral invariant from the knot group

This is a developed version of the talk in 9 May, 2008 entitled “Numerical invariants from knot groups”. Let K be a knot in S, G(K) the knot group of K, and G′(K) the commutator subgroup of G(K).

On unions of knots

Introduction If two knots ιc and κ with a common arc <#, of which K, lies inside a cube Q and πf outside of it, a lying naturally on the boundary of Q, are joined together along oίy that is, if a is

Unknotting numbers of 2‐spheres in the 4‐sphere

We compare two naturally arising notions of ‘unknotting number’ for 2‐spheres in the 4‐sphere: namely, the minimal number of 1‐handle stabilizations needed to obtain an unknotted surface, and the

Identifying tunnel number one knots

Let $K$ be a knot in $S^{3}$ . The tunnel number $t(K)$ of $K$ is the minimal number of mutually disjoint arcs $\{\tau_{i}\}$ “properly embedded” in the pair $(S^{3}, K)$ such that the complement of

A Lower Bound on Unknotting Number*

In this paper the authors use a modified Wirtinger presentation to give a lower bound on the unknotting number of a knot in S3.

Knot groups

  • Teruhisa KADOKAMI School of Mechanical Engineering
  • 1965