KNOT QUANDLES AND INFINITE CYCLIC COVERING SPACES

Let K be an n-dimensional knot (n >= l), 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\K. We show that the set consisting of homomorphisms Q(K)-> Zq([t +/- 1])/J is isomorphic to Z(q)[(t +/- l)]/J circle plus Hom(z[t +/- l]), (C-infinity(K)), Z(q)[(t +/- l)]/J) as Z[t +/- l]-modules. Here, Homz[t +/- l] (H-l (C-infinity(K)), Z(q)[(t +/- l)]/J) denotes the set consisting of Z[t +/- l]-homomorphisms H-1(C-infinity(K)) -> Zq([t +/- l)]/J.