The bipolar filtration of topologically slice knots

Jae Choon Cha; Min Hoon Kim

doi:10.1016/j.aim.2021.107868

The bipolar filtration of topologically slice knots

Jae Choon Cha, Min Hoon Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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 L² ρ-invariants and infinitely many Heegaard Floer correction term d-invariants.

Original language	English
Article number	107868
Journal	Advances in Mathematics
Volume	388
DOIs	https://doi.org/10.1016/j.aim.2021.107868
State	Published - 17 Sep 2021

Bibliographical note

Publisher Copyright:
© 2021 Elsevier Inc.

Keywords

Bipolar filtration
Cheeger-Gromov invariants
Heegaard Floer invariants
Knot concordance

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AB - 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 L2 ρ-invariants and infinitely many Heegaard Floer correction term d-invariants.

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The bipolar filtration of topologically slice knots

Abstract

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Keywords

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