The Hotel of Algebraic Surgery

Abstract

We revisit the algebraic surgery theory and especially the proof of the total surgery obstruction.<br /> The total surgery obstruction was defined by Ranicki for a finite n-dimensional Poincaré complex X as an element in a certain abelian group with the property that for n≥5 it vanishes if and only if X is homotopy equivalent to a closed n-dimensional manifold. <br /> This thesis adds details that were missing in the original sources and provides a self-contained proof. <br /> In order to make the proof and the underlying algebraic surgery theory more easily accessible, the proof is presented in various levels with each level supplying more elaborate details.