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Sign refinement for combinatorial link Floer homology

Étienne Gallais

Algebraic & Geometric Topology 8 (2008) 1581–1592
Abstract

Link Floer homology is an invariant for links which has recently been described entirely in a combinatorial way. Originally constructed with mod 2 coefficients, it was generalized to integer coefficients thanks to a sign refinement. In this paper, thanks to the spin extension of the permutation group we give an alternative construction of the combinatorial link Floer chain complex associated to a grid diagram with integer coefficients. In particular we prove that the sign refinement comes from a 2–cohomological class corresponding to the spin extension of the permutation group.

Keywords
link floer homology, sign refinement
Mathematical Subject Classification 2000
Primary: 57R58
References
Publication
Received: 4 July 2007
Revised: 30 May 2008
Accepted: 3 August 2008
Published: 15 September 2008
Authors
Étienne Gallais
Laboratoire de Mathématiques Jean Leray (LMJL)
UFR Sciences et Techniques
2 rue de la Houssinière - BP 92208
44 322 Nantes Cedex 3
France
http://www.math.sciences.univ-nantes.fr/~gallais/