Algebraic & Geometric Topology

Singular link Floer homology

Benjamin Audoux

Full-text: Open access


We define a grid presentation for singular links, ie links with a finite number of rigid transverse double points. Then we use it to generalize link Floer homology to singular links. Besides the consistency of its definition, we prove that this homology is acyclic under some conditions which naturally make its Euler characteristic vanish.

Article information

Algebr. Geom. Topol., Volume 9, Number 1 (2009), 495-535.

Received: 1 April 2008
Revised: 2 November 2008
Accepted: 11 February 2009
First available in Project Euclid: 20 December 2017

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

singular links link Floer homology


Audoux, Benjamin. Singular link Floer homology. Algebr. Geom. Topol. 9 (2009), no. 1, 495--535. doi:10.2140/agt.2009.9.495.

Export citation


  • B Audoux, Généralisation de l'homologie de Heegaard Floer aux entrelacs singuliers & raffinement de l'homologie de Khovanov aux entrelacs restreints, PhD thesis, Université Toulouse III – Paul Sabatier (2007)
  • J S Birman, X-S Lin, Knot polynomials and Vassiliev's invariants, Invent. Math. 111 (1993) 225–270
  • P R Cromwell, Embedding knots and links in an open book. I. Basic properties, Topology Appl. 64 (1995) 37–58
  • I A Dynnikov, Arc-presentations of links: monotonic simplification, Fund. Math. 190 (2006) 29–76
  • E Gallais, Sign refinment for combinatorial link Floer homology
  • L H Kauffman, Invariants of graphs in three-space, Trans. Amer. Math. Soc. 311 (1989) 697–710
  • M Khovanov, A categorification of the Jones polynomial, Duke Math. J. 101 (2000) 359–426
  • C Manolescu, P Ozsváth, S Sarkar, A combinatorial description of knot Floer homology
  • C Manolescu, P Ozsváth, Z Szabó, D Thurston, On combinatorial link Floer homology
  • P Ozsváth, A Stipsicz, Z Szabó, Floer homology and singular knots
  • P Ozsváth, Z Szabó, Holomorphic disks and knot invariants, Adv. Math. 186 (2004) 58–116
  • J Rasmussen, Floer homology and knot complements, PhD thesis, Harvard University (2003)
  • N Shirokova, On the classification of Floer-type theories