Seifert cohomology of trees

Abstract

To every tree we associate a filtered cochain complex. Its cohomology and the corresponding spectral sequence have clear combinatorial description. If a tree is the Dynkin diagram of a simple plane curve singularity, the graded Euler characteristic of this complex coincides with the Alexander polynomial of the link. In this case we also point the relation to the Heegard-Floer homology theory, constructed by P. Ozsvath and Z. Szabo.