• 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},
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

• Mathematics
• 2010
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).
• Mathematics
• 1957
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
• Mathematics
Journal of Topology
• 2021
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
• Mathematics
• 1996
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
• Mathematics
• 2006
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