Knot Floer homology obstructs ribbon concordance

Pages 931-947 from Volume 190 (2019), Issue 3 by Ian Zemke

Abstract

We prove that the map on knot Floer homology induced by a ribbon concordance is injective. As a consequence, we prove that the Seifert genus is monotonic under ribbon concordance. Generalizing theorems of Gabai and Scharlemann, we also prove that the Seifert genus is super-additive under band connected sums of arbitrarily many knots. Our results give evidence for a conjecture of Gordon that ribbon concordance is a partial order on the set of knots.

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      mrclass = {57R58 (57M27)},
      mrnumber = {3950650},
      doi = {10.4171/QT/124},
      url = {https://doi.org/10.4171/QT/124},
      zblnumber = {07068343},
      }
  • [ZemCFLTQFT] Go to document I. Zemke, "Link cobordisms and functoriality in link Floer homology," J. Topol., vol. 12, iss. 1, pp. 94-220, 2019.
    @ARTICLE{ZemCFLTQFT,
      author = {Zemke, Ian},
      title = {Link cobordisms and functoriality in link {F}loer homology},
      journal = {J. Topol.},
      fjournal = {Journal of Topology},
      volume = {12},
      year = {2019},
      number = {1},
      pages = {94--220},
      issn = {1753-8416},
      mrclass = {57M27 (57M25 57R56)},
      mrnumber = {3905679},
      mrreviewer = {Daniel D. Moskovich},
      doi = {10.1112/topo.12085},
      url = {https://doi.org/10.1112/topo.12085},
      zblnumber = {07055381},
      }

Keywords
, , ,
Mathematical Subject Classification
Primary: , , ,
DOI
https://doi.org/10.4007/annals.2019.190.3.5
MR
4024565
zbMATH
07128143
Milestones
Received: 17 February 2019
Revised: 17 July 2019
Accepted: 28 August 2019
Published online: 28 October 2019

Authors

Ian Zemke

Princeton University Princeton, NJ