Structure in the bipolar filtration of topologically slice knots

Abstract

Let T denote the group of smooth concordance classes of topologically sice knots. We show that the first quotient in the bipolar filtration of T (i.e. 0-bipolar knots modulo 1-bipolar knots) has infinite rank, even modulo Alexander polynomial one knots. Any 0-bipolar knot has vanishing tau-, epsilon-, and s-invariants. We prove the result using d-invariants associated to the 2-fold branched covers of knot complements.

9 pages, 5 figures

References in corpus (2)

• Filtering smooth concordance classes of topologically slice knots
• Covering link calculus and the bipolar filtration of topologically slice links

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