English

The bipolar filtration of topologically slice knots

Geometric Topology 2021-06-29 v2

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 L2L^2 ρ\rho-invariants and infinitely many Heegaard Floer correction term dd-invariants.

Keywords

Cite

@article{arxiv.1710.07803,
  title  = {The bipolar filtration of topologically slice knots},
  author = {Jae Choon Cha and Min Hoon Kim},
  journal= {arXiv preprint arXiv:1710.07803},
  year   = {2021}
}

Comments

27 pages, 12 figures; the introduction has been largely revised and expositions have been improved by incorporating referee's comments; to appear in Advances in Mathematics