## Algebraic & Geometric Topology

### Sign refinement for combinatorial link Floer homology

Étienne Gallais

#### 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 8, Number 3 (2008), 1581-1592.

Dates
Revised: 30 May 2008
Accepted: 3 August 2008
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513796898

Digital Object Identifier
doi:10.2140/agt.2008.8.1581

Mathematical Reviews number (MathSciNet)
MR2443255

Zentralblatt MATH identifier
1149.57043

Subjects
Primary: 57R58: Floer homology

#### Citation

Gallais, Étienne. Sign refinement for combinatorial link Floer homology. Algebr. Geom. Topol. 8 (2008), no. 3, 1581--1592. doi:10.2140/agt.2008.8.1581. https://projecteuclid.org/euclid.agt/1513796898

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