. G T / 0 50 52 33 v 1 1 2 M ay 2 00 5 NEW TOPOLOGICALLY SLICE KNOTS
نویسنده
چکیده
In the early 1980’s Mike Freedman showed that all knots with trivial Alexander polynomial are topologically slice (with fundamental group Z). This paper contains the first new examples of topologically slice knots. In fact, we give a sufficient homological condition under which a knot is slice with fundamental group Z⋉Z[1/2]. These two fundamental groups are known to be the only solvable ribbon groups. Our homological condition implies that the Alexander polynomial equals (t−2)(t−2) but also contains information about the metabelian cover of the knot complement (since there are many non-slice knots with this Alexander polynomial).
منابع مشابه
Slice Knots with Distinct Ozsváth-szabó and Rasmussen Invariants
As proved by Hedden and Ording, there exist knots for which the Ozsváth-Szabó and Rasmussen smooth concordance invariants, τ and s, differ. The Hedden-Ording examples have nontrivial Alexander polynomials and are not topologically slice. It is shown in this note that a simple manipulation of the Hedden-Ording examples yields a topologically slice Alexander polynomial one knot for which τ and s ...
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In the early 1980’s Mike Freedman showed that all knots with trivial Alexander polynomial are topologically slice (with fundamental group Z). This paper contains the first new examples of topologically slice knots. In fact, we give a sufficient homological condition under which a knot is slice with fundamental group Z ⋉ Z[1/2]. These two fundamental groups are known to be the only solvable ribb...
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