English

Structure in the bipolar filtration of topologically slice knots

Geometric Topology 2016-01-20 v1

Abstract

Let T denote the group of smooth concordance classes of topologically sice knots. We show that the first quotient in the bipolar filtration of T (i.e. 0-bipolar knots modulo 1-bipolar knots) has infinite rank, even modulo Alexander polynomial one knots. Any 0-bipolar knot has vanishing tau-, epsilon-, and s-invariants. We prove the result using d-invariants associated to the 2-fold branched covers of knot complements.

Keywords

Cite

@article{arxiv.1208.5788,
  title  = {Structure in the bipolar filtration of topologically slice knots},
  author = {Tim D. Cochran and Peter D. Horn},
  journal= {arXiv preprint arXiv:1208.5788},
  year   = {2016}
}

Comments

9 pages, 5 figures