Blanchfield and Seifert algebra in high dimensional knot theory
Novikov [12] initiated the study of the algebraic properties of quadratic forms over polynomial extensions by a far-reaching analogue of the Pontrjagin-Thom transversality construction of a Seifert surface of a knot and the infinite cyclic cover of the knot exterior. In this paper the analogy is applied to explain the relationship between the Seifert forms over a ring with involution A and Blanchfield forms over the Laurent polynomial extension A[z, z]. The rings A and A[z, z] correspond to the two ways of associating algebraic invariants to an n-knot k : S ⊂ S with A = Z : (i) The Z[z, z]-module invariants of the canonical infinite cyclic cover M = pR of the exterior of k M = cl.(S\k(S)×D) ⊂ S with k(S) × D ⊂ S a regular neighbourhood of k(S) in S, p : M → S a map inducing an isomorphism p : H(S) ∼= H(M), and ∂M = S × S. (ii) The Z-module invariants of a codimension 1 submanifold N ⊂ S with boundary ∂N = k(S) ⊂ S ,
Structure in the classical knot concordance group

Abstract
We provide new information about the structure of the
abelian group of topological concordance classes of knots in $S^3$. One
consequence is that there is a subgroup of infinite rank consisting
entirely of knots with vanishing Casson-Gordon invariants but whose
non-triviality is detected by von Neumann signatures.

Meromorphic function sharing a small function with a homogeneous differential polynomial
Abstract In this paper, we consider a Brück-type result for a homogeneous differential polynomial generated by a meromorphic function.