The bipolar filtration of topologically slice knots

Jae Choon Cha; Min Hoon Kim

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arXiv · 1710.07803

The bipolar filtration of topologically slice knots

Jae Choon Cha·Min Hoon Kim

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Abstract

The bipolar filtration of Cochran, Harvey and Horn presents a framework of the study of deeper structures in the smooth concordance group of topologically slice knots. We show that the graded quotient of the bipolar filtration of topologically slice knots has infinite rank at each stage greater than one. To detect nontrivial elements in the quotient, the proof simultaneously uses higher order amenable Cheeger-Gromov $L^2$ $\rho$-invariants and infinitely many Heegaard Floer correction term $d$-invariants.

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Jae Choon Cha, Min Hoon Kim. 2017-10-21. The bipolar filtration of topologically slice knots. https://arxiv.org/abs/1710.07803

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