arXiv math/04043832004-04-21math.AT

The algebraic theory of Kreck surgery

Jörg Sixt

备注：: 112 pages. Taken from the author's 2004 Edinburgh University doctoral thesis. See also http://www.maths.ed.ac.uk/~sixt

英文摘要：

In the 1980s Matthias Kreck developed a modified surgery theory with obstructions in a hardly understood monoid $l_n(Z[π])$. This paper presents a couple of purely algebraic tools to find out whether an element in $l_{2q}(R)$ is "elementary" i.e. whether a Kreck surgery problem leads to an $h$-cobordism or not.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

4-流形上的稳定等价关系

Stable equivalence relations on 4-manifolds

University of Southampton（南安普顿大学）；University of Glasgow（格拉斯哥大学）；Universität Bonn（波恩大学）

该研究结合改进式与经典手术理论，研究4-流形的多种稳定等价关系，证明阿贝尔基本群的闭可定向同伦等价4-流形稳定微分同胚，给出稳定同胚消去定理对应版本及相关代数障碍。

2025-10-09math.ATmath.GT

The structure set of an arbitrary space, the algebraic surgery exact sequence and the total surgery obstruction

An introduction to the applications of algebraic surgery to the structure theory of high-dimensional topological manifolds.

2001-11-30math.ATmath.GT

Foundations of algebraic surgery

An elementary introduction to the principles of algebraic surgery.

2001-11-30math.ATmath.GT

An introduction to algebraic surgery

Browder-Novikov-Sullivan-Wall surgery theory investigates the homotopy types of manifolds, using a combination of algebra and topology. It is the aim of these notes to provide an introduction to the more algebraic aspects of the theory (such as the Wall surgery obstruction groups), without losing sight of the geometric motivation.

2000-08-09math.ATmath.GT

Algebraic Poincare cobordism

This paper is an introduction to the use of the cobordism of chain complexes with Poincaré duality in surgery theory. It is a companion to the author's paper "An introduction to algebraic surgery" math.AT/0008071 (to appear in Volume 2 of Surveys in Surgery Theory, Ann. of Maths. Studies, Princeton, 2001) which is an introduction to algebraic surgery using forms and formations.

2000-08-30math.ATmath.GT

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…

2018-05-19math.ATmath.GT

更多相关论文收起更多论文

区间-球面模型结构

Interval-sphere model structures

本文提出一种紧致组合模型范畴结构，将区间手术形式化为真正的模型范畴胞腔附着，并揭示余纤维性与持续性理论中驯顺性及代数紧致性的内在联系。

2025-07-03math.AT

Controlled surgery and $\mathbb{L}$-homology

This paper presents an alternative approach to controlled surgery obstructions. The obstruction for a degree one normal map $(f,b): M^n \rightarrow X^n$ with control map $q: X^n \rightarrow B$ to complete controlled surgery is an element $σ^c (f, b) \in H_n (B, \mathbb{L})$, where $M^n, X^n$ are topological manifolds of dimension $n \geq 5$. Our proof uses essentially the geometrically defined $\mathbb{L}$-spectrum as described by Nicas (going back to Quinn) and some well known homotopy theory. We also outline the construction of the algebraically defined obstruction, and we explicitly describ…

2020-04-21math.ATmath.GT

自旋4-流形稳定微分同胚的代数判据

Algebraic criteria for stable diffeomorphism of spin 4-manifolds

University of Southampton（南安普顿大学）；University of Glasgow（格拉斯哥大学）；Max Planck Institut für Mathematik（马克斯·普朗克数学研究所）

本文研究闭连通自旋4-流形的稳定微分同胚分类，提出次障碍和三级障碍与代数不变量的关联猜想，对多类基本群证明了猜想，并给出基本群为$\mathbb{Z} \times \mathbb{Z}/2$的自旋4-流形的完整代数稳定分类。

2024-06-06math.ATmath.GT

A survey of Wall's finiteness obstruction

Wall's finiteness obstruction is an algebraic K-theory invariant which decides if a finitely dominated space is homotopy equivalent to a finite CW complex. The object of this survey is to describe the invariant (which was first formulated in 1965) and some of its many applications to the surgery classification of manifolds.

2000-08-09math.ATmath.GT