Hodge-type structures as link invariants

Details Hodge-type structures as link invariants Hodge-type structures as link invariants

2010-05-12

arxiv.org/abs/1005.2084v2

Mathematics

Geometric Topology

22 pages. A difficult to spot mistake corrected in the formula in Corollary 4.4.9(a)

Scientific paper

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 $S^3$. 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.

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