2026/07/28 by David Cimasoni, Anthony Conway, Gaetan Simian · 1 citation
Mathematics · #math.GT
Algebraic concordance of knots can be understood from the perspective of Seifert matrices, Blanchfield forms, and homology surgery. We initiate a systematic study of algebraic concordance for links from each of these viewpoints. The present article is concerned with algebraic concordance from the perspective of homology surgery and Blanchfield forms, whereas a companion article by the third named author focuses on C-complexes and generalised Seifert matrices. The outcome of the present work consists of two obstructions to μ-component links being concordant. The first obstruction, called the homology surgery invariant, takes values in the Witt group of hermitian forms over the field of fractions Q of ℤ[ℤμ]. The second obtruction, called the Blanchfield invariant, takes values in a Witt group of Q/ℤ[ℤμ]-valued hermitian linking forms. For μ≤ 2, we describe these invariants in terms of generalised Seifert matrices.