논문KCI 등재
Revisit to Alexander Modules of 2-generator Knots in the 3-sphere
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It is known that a 2-generator knot K has a cyclic Alexander module Z[t,t−1]/(∆(t)) where ∆(t) is the Alexander polynomial of K. In this paper we explicitly show how to reduce 2-generator Alexander modules to cyclic ones by using Chiswell, Glass and Wilsons presentations of 2-generator knot groupswhere ab = bab−1. < x,y | (xα1)yγ1 ,··· ,(xαk)yγk >
Abstract
It is known that a 2-generator knot K has a cyclic Alexander module Z[t,t−1]/(∆(t)) where ∆(t) is the Alexander polynomial of K. In this paper we explicitly show how to reduce 2-generator Alexander modules to cyclic ones by using Chiswell, Glass and Wilsons presentations of 2-generator knot groupswhere ab = bab−1. < x,y | (xα1)yγ1 ,··· ,(xαk)yγk >
참고문헌 (9)
- G. Berde, "Knots" (2003), Walter de Gruyter
- I.M. Chiswell, "Residual nilpotence and ortdering in one-relator groups and knot groups", arXiv:1405.0994v2, ~
- Taizo Kanenobu, "Classification of a family of ribbon 2-knots with trivial Alexander polynomial", 대한수학회논문집, 33(2), pp.591~604 (2018), 대한수학회
- C. McA. Gordon, "Knot theory", pp.1~60 (1978), Springer Ver-lag
- R. Lyndon, "Combinatorial Group Theory" (1977), Springer-Verlag
- W. Magnus, "Combinatorial group theory" (1966), Wiley
- J. Milnor, "Infinite cyclic coverings", Conference on the Topology of Manifolds, pp.115133~ (1968), Prindle, Weber, and Schmidt
- H.J. Song, "Infinite cyclic covering spaces of (1,1)-knot complements", preparation, ~
- H.J. Song, "Knots with cyclic Alexander modules", preparation, ~
관련 논문AI추천
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