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The bipolar filtration introduced by T. Cochran, S. Harvey, and P. Horn is aframework for the study of smooth concordance of topologically slice knots andlinks. It is known that there are topologically slice 1-bipolar knots which arenot 2-bipolar. For knots, this is the highest known level at which thefiltration does not stabilize. For the case of links with two or morecomponents, we prove that the filtration does not stabilize at any level: forany n, there are topologically slice links which are n-bipolar but not(n+1)-bipolar. In the proof we describe an explicit geometric constructionwhich raises the bipolar height of certain links exactly by one. We show thisusing the covering link calculus. Furthermore we discover that the bipolarfiltration of the group of topologically slice string links modulo smoothconcordance has a rich algebraic structure.

Covering link calculus and the bipolar filtration of topologically slice links