Topologically slice knots with nontrivial Alexander polynomial. (English) Zbl 1254.57008
The authors use the correction term of P. Ozsváth and Z. Szabó [Adv. Math. 173, No. 2, 179–261 (2003; Zbl 1025.57016)] to define an obstruction to a topologically (locally flat) slice knot being smoothly concordant to a knot with Alexander polynomial 1. Using this obstruction, they show that if \(\mathcal{C}_{T}\) denotes the subgroup of the smooth knot concordance group generated by topologically slice knots and \(\mathcal{C} _{\Delta}\) denotes the subgroup of \(\mathcal{C}_{T}\) generated by knots with trivial Alexander polynomial, then the quotient \(\mathcal{C}_{T} /\mathcal{C}_{\Delta}\) is infinitely generated. They also exhibit a family of 2-component links that are topologically concordant to boundary links, but not smoothly so.
Reviewer: Lorenzo Traldi (Easton)
MSC:
| 57M25 | Knots and links in the \(3\)-sphere (MSC2010) |
Citations:
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