θ-curves inducing two different knots with the same 2-fold branched covering spaces
Kim, Soo Hwan ; Kim, Yangkok
Bollettino dell'Unione Matematica Italiana, Tome 6-A (2003), p. 199-209 / Harvested from Biblioteca Digitale Italiana di Matematica
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For a knot K with a strong inversion i induced by an unknotting tunnel, we have a double covering projection Π:S3→S3/i branched over a trivial knot Π⁢fix⁢i, where fix⁢i is the axis of i. Then a set Π⁢fix⁢i∪K is called a θ-curve. We construct θ-curves and the Z2⊕Z2 cyclic branched coverings over θ-curves, having two non-isotopic Heegaard decompositions which are one stable equivalent.

Per un nodo K con un'inversione forte i indotta da un tunnel di scioglimento abbiamo una proiezione Π:S3→S3/i che è un ricoprimento doppio ramificato sopra un nodo banale Π⁢fix⁢i, dove fix⁢i è l'asse i. Allora un insieme Π⁢fix⁢i∪K è chiamato θ-curva. Costruiamo θ-curve e i ricoprimenti Z2⊕Z2 ciclici ramificati sopra θ-curve, che hanno due decomposizioni di Heegaard non isotopiche che sono uno stabilmente equivalenti.

Publié le : 2003-02-01
@article{BUMI_2003_8_6B_1_199_0,
     author = {Soo Hwan Kim and Yangkok Kim},
     title = {$\theta$-curves inducing two different knots with the same $2$-fold branched covering spaces},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {6-A},
     year = {2003},
     pages = {199-209},
     zbl = {1150.57002},
     mrnumber = {1955705},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2003_8_6B_1_199_0}
}

Kim, Soo Hwan; Kim, Yangkok. $\theta$-curves inducing two different knots with the same $2$-fold branched covering spaces. Bollettino dell'Unione Matematica Italiana, Tome 6-A (2003) pp. 199-209. http://gdmltest.u-ga.fr/item/BUMI_2003_8_6B_1_199_0/

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