The bipolar filtration of topologically slice knots

Cha, Jae Choon; Kim, Min Hoon

doi:10.1016/j.aim.2021.107868

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The bipolar filtration of topologically slice knots

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Cha, Jae Choon
Max Planck Institute for Mathematics, Max Planck Society;

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Kim, Min Hoon
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.1016/j.aim.2021.107868
(Publisher version)

https://doi.org/10.48550/arXiv.1710.07803
(Preprint)

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Citation

Cha, J. C., & Kim, M. H. (2021). The bipolar filtration of topologically slice knots. Advances in Mathematics, 388: 107868. doi:10.1016/j.aim.2021.107868.

Cite as: https://hdl.handle.net/21.11116/0000-0009-FE68-5

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.