ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

6. Topology

1991 MS Classification: 57 Kearton, Cherry, University of Durham, England: Alexander ideals of classical knots. A polynomial f(t) ∈ Z [t, t^{−1}] is the i th Alexander polynomial of some classical knot if and only if f(1) = ±1 and f (t^{−1}) = t^{2r} f(t) for some r ∈ Z. This result was proved by H. Seifert in 1934. In joint work with S. M. J. Wilson, I show that an ideal E(t) of Z [t, t^{−1}] is the i th Alexander ideal of some classical knot, for some i, if and only if E(1) = Z and E (t^{−1}) = E(t).