Blanchfield and Seifert algebra in high-dimensional boundary link theory I: Algebraic K-theory

Blanchfield and Seifert algebra in high dimensional knot theory

Novikov 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 and Blanchfield forms over the Laurent polynomial extension.

Invariants of Boundary Link Cobordism II. The Blanchfield-Duval Form

We use the Blanchfield-Duval form to define complete invariants for the cobordism group C_{2q-1}(F_μ) of (2q-1)-dimensional μ-component boundary links (for q\geq2). The author solved the same problem in math.AT/0110249 via Seifert forms. Although Seifert forms are convenient in explicit computations, the Blanchfield-Duval form is more intrinsic and appears naturally in homology surgery theory. The free cover of the complement of a link is constructed by pasting together infinitely many copies of the complement of a μ-component Seifert surface. We prove that the algebraic analogue of this const…

链环的代数协边群

Algebraic concordance groups for links

研究利用广义Seifert矩阵族定义链环的代数协边群，借此恢复相关不变性，并用于研究群的同构类型。

Codimension 2 embeddings, algebraic surgery and Seifert forms

We study the cobordism of manifolds with boundary, and its applications to codimension 2 embeddings $M^m\subset N^{m+2}$, using the method of the algebraic theory of surgery. The first main result is a splitting theorem for cobordisms of algebraic Poincaré pairs, which is then applied to describe the behaviour on the chain level of Seifert surfaces of embeddings $M^{2n-1} \subset S^{2n+1}$ under isotopy and cobordism. The second main result (update: which is false) is that the $S$-equivalence class of a Seifert form is an isotopy invariant of the embedding, generalizing the Murasugi--Levine re…

Algebraic and combinatorial codimension-1 transversality

The Waldhausen construction of Mayer-Vietoris splittings of chain complexes over an injective generalized free product of group rings is extended to a combinatorial construction of Seifert-van Kampen splittings of CW complexes with fundamental group an injective generalized free product.

Seifert-van Kampen定理与驯顺基本群上的Frobenius作用

A Seifert-van Kampen Theorem and the Frobenius Action on Tame Fundamental Groups

本文通过Harbater形式粘贴证明Seifert-van Kampen定理，给出Galois群对驯顺基本群生成元作用的纯代数描述，并显式计算射影直线去掉$n$个点的驯顺基本群。