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