Structure in the bipolar filtration of topologically slice knots

Tim D. Cochran; Peter D. Horn

doi:10.2140/agt.2015.15.415

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arXiv · 1208.5788

Structure in the bipolar filtration of topologically slice knots

Tim D. Cochran·Peter D. Horn

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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.

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Tim D. Cochran, Peter D. Horn. 2012-08-28. Structure in the bipolar filtration of topologically slice knots. https://doi.org/10.2140/agt.2015.15.415

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