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

TL;DR

This paper introduces algebraic surgery techniques and their applications to understanding the structure of high-dimensional topological manifolds, focusing on the algebraic surgery exact sequence and the total surgery obstruction.

Contribution

It presents a novel application of algebraic surgery to the structure theory of high-dimensional manifolds, including the algebraic surgery exact sequence and total surgery obstruction.

Findings

Development of the algebraic surgery exact sequence

Identification of the total surgery obstruction

Enhanced understanding of manifold structures

Abstract

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