Knot quandles and infinite cyclic covering spaces

Inoue, Ayumu

Inoue, Ayumu

Kodai Math. J., Tome 33 (2010) no. 1, p. 116-122 / Harvested from Project Euclid

Résumé

Let K be an n-dimensional knot (n ≥ 1), Q(K) the knot quandle of K, Z_q[t^±1]/J an Alexander quandle, and C_∞(K) the infinite cyclic covering space of Sⁿ⁺² $\backslash$ K. We show that the set consisting of homomorphisms Q(K) → Z_q[t^±1]/J is isomorphic to Z_q[t^±1]/J ⊕ Hom_Z[t^±1] (H₁(C_∞(K)), Z_q[t^±1]/J) as Z[t^±1]-modules. Here, Hom_Z[t^±1](H₁(C_∞(K)), Z_q[t^±1]/J) denotes the set consisting of Z[t^±1]-homomorphisms H₁(C_∞(K)) → Z_q[t^±1]/J.

Publié le : 2010-03-15
Classification:

@article{1270559161,
     author = {Inoue, Ayumu},
     title = {Knot quandles and infinite cyclic covering spaces},
     journal = {Kodai Math. J.},
     volume = {33},
     number = {1},
     year = {2010},
     pages = { 116-122},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1270559161}
}

Inoue, Ayumu. Knot quandles and infinite cyclic covering spaces. Kodai Math. J., Tome 33 (2010) no. 1, pp.  116-122. http://gdmltest.u-ga.fr/item/1270559161/