English

Topologically slice knots with nontrivial Alexander polynomial

Geometric Topology 2013-12-24 v3

Abstract

Let C_T be the subgroup of the smooth knot concordance group generated by topologically slice knots and let C_D be the subgroup generated by knots with trivial Alexander polynomial. We prove the quotient C_T/C_D is infinitely generated, and uncover similar structure in the 3-dimensional rational spin bordism group. Our methods also lead to the construction of links that are topologically, but not smoothly, concordant to boundary links.

Keywords

Cite

@article{arxiv.1001.1538,
  title  = {Topologically slice knots with nontrivial Alexander polynomial},
  author = {Matthew Hedden and Charles Livingston and Daniel Ruberman},
  journal= {arXiv preprint arXiv:1001.1538},
  year   = {2013}
}

Comments

27 pages, 7 figures. Clarified discussion of Spinc structures; fixed some typos

R2 v1 2026-06-21T14:32:53.687Z