Real Seifert forms, Hodge numbers and Blanchfield pairings

TL;DR

This survey explores the relationships between singularity invariants, Hodge theory, and link pairings, highlighting the role of Hermitian Variation Structures in unifying these concepts.

Contribution

It synthesizes connections between Picard--Lefschetz invariants, Blanchfield pairings, and Hermitian Variation Structures, providing a comprehensive overview of their interplay.

Findings

Unified perspective on singularity invariants and link pairings

Emphasis on Hermitian Variation Structures as a unifying framework

Clarification of the role of Hodge numbers in these connections

Abstract

In this survey article we present connections between Picard--Lefschetz invariants of isolated hypersurface singularities and Blanchfield forms for links. We emphasize the unifying role of Hermitian Variation Structures introduced by N\'emethi.