Surgery obstruction groups

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1 Introduction

The surgery obstruction groups L_n(\bZ\pi, w) of C.T.C. Wall [Wall1999], [Wall1976] 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.

The groups L_n(R\pi, w) 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

On the classification of hermitian forms: VI, Wall (1976)


2 References

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