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PreprintarXiv licencearXiv

Relative knot concordance

  • Vyacheslav Krushkal
  • Ryan Stees
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Abstract

Motivated by the relative-slice problem in $4$-manifold topology, we define for a knot R the notion of a relative knot concordance group π’žR and analyze the structure of its algebraic analogue π’œπ’žR modulo torsion. Using Milnor signatures, we show that π’œπ’žR has infinite rank for every R. We also show that any prescribed finite set of natural numbers can be realized as orders of elements in a single relative concordance group.

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Cite

BibTeXRIS
BibTeX
@misc{krushkal2026relative,
  title = {{Relative knot concordance}},
  author = {Vyacheslav Krushkal and Ryan Stees},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.19467},
  eprint = {2610.19467},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.19467},
}
RIS
TY  - UNPB
TI  - Relative knot concordance
AU  - Vyacheslav Krushkal
AU  - Ryan Stees
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.19467
UR  - https://arxiv.org/abs/2610.19467
AB  - Motivated by the relative-slice problem in $4$-manifold topology, we define for a knot R the notion of a relative knot concordance group π’ž_R and analyze the structure of its algebraic analogue π’œπ’ž_R modulo torsion. Using Milnor signatures, we show that π’œπ’ž_R has infinite rank for every R. We also show that any prescribed finite set of natural numbers can be realized as orders of elements in a single relative concordance group.
ER  -