2007/06/21 by Étienne Gallais
Mathematics · #Advanced Combinatorial Mathematics #Cyclic permutation #Extension (predicate logic) #Floer homology #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Invariant (physics) #Link (geometry) #Partial permutation #Permutation (music) #Sign (mathematics) #math.GT
paper · pdf · doi:10.2140/agt.2008.8.1581
published as Algebr. Geom. Topol. 8 (2008) 1581-1592 · 17 pages, 10 figures. correction of the Alexander grading and of the formula of lemma 5.2 of the sign refinement
arxiv created 2007/06/21 · openalex publication_date 2008/09/15 · arxiv updated 2014/09/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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. 57R58