Surgery obstruction groups

Revision as of 11:05, 8 June 2010

1 Introduction

\newcommand{\bZ}{\mathbf Z} The surgery obstruction groups ${{Authors|Hambleton}} == Introduction == <wikitex>; \newcommand{\bZ}{\mathbf Z} The surgery obstruction groups $L_n(\bZ\pi, w)$ of C.T.C. Wall \cite{wall-book}, \cite{wall-VI} contain the obstructions to doing surgery on a degree 1 normal map $(f,b)\colon M \to X$ to obtain a homotopy equivalence. In this setting, $X$ is an $n$-dimensional Poincar\'e complex $\pi = \pi_1(X, x_0)$ is the fundamental group of $X$, and $w = w_1(X)$ is the first Stiefel-Whitney class depend on a coefficient ring $R$, a discrete group $\pi$ and an orientation character $w\colon \pi \to \{\pm 1\}$. In general the surgery obstruction groups are abelian groups. For finite groups $\pi$ the $L$-groups are finitely-generated and the only torsion is $-primary. [[Media:Filename.pdf|A Guide to the Calculation of Surgery Obstruction Groups, Hambleton & Taylor (2000), pp. 1-3]] </wikitex> == References == {{#RefList:}} [[Category:Theory]] {{Stub}}L_n(\bZ\pi, w)$ of C.T.C. Wall [wall-book], [wall-VI] contain the obstructions to doing surgery on a degree 1 normal map $(f,b)\colon M \to X$ to obtain a homotopy equivalence. In this setting, $X$ is an $n$-dimensional Poincar\'e complex $\pi = \pi_1(X, x_0)$ is the fundamental group of $X$, and $w = w_1(X)$ is the first Stiefel-Whitney class depend on a coefficient ring $R$, a discrete group $\pi$ and an orientation character $w\colon \pi \to \{\pm 1\}$. In general the surgery obstruction groups are abelian groups. For finite groups $\pi$ the $L$-groups are finitely-generated and the only torsion is $2$-primary.

A Guide to the Calculation of Surgery Obstruction Groups, Hambleton & Taylor (2000), pp. 1-3

2 References

• [wall-VI] Template:Wall-VI
• [wall-book] Template:Wall-book