2010/05/12 by Borodzik, Maciej, Nemethi, Andras
#14D07 #14H20 #32S25 #57M25 #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1005.2084
Based on some analogies with the Hodge theory of isolated hypersurface singularities, we define Hodge-type numerical invariants (called H-numbers) of any, not necessarily algebraic, link in S3. They contain the same information as the (normalized) real Seifert matrix. We study their basic properties, we express the Tristram-Levine signatures and the higher order Alexander polynomial in terms of them. Motivated by singularity theory, we also introduce the spectrum of the link (determined from these H-numbers), and we establish some semicontinuity properties for it.