Surgery obstruction groups
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1 Introduction
The surgery obstruction groups of C.T.C. Wall [Wall1999], [Wall1976] contain the obstructions to doing surgery on a degree 1 normal map to obtain a homotopy equivalence. In this setting, is an -dimensional Poincar\'e complex is the fundamental group of , and is the first Stiefel-Whitney class.
The groups depend on a coefficient ring , a discrete group and an orientation character . In general the surgery obstruction groups are abelian groups. For finite groups the -groups are finitely-generated and the only torsion is -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
- [Wall1976] C. T. C. Wall, Classification of Hermitian Forms. VI. Group rings, Ann. of Math. (2) 103 (1976), no.1, 1–80. MR0432737 (55 #5720) Zbl 0328.18006
- [Wall1999] C. T. C. Wall, Surgery on compact manifolds, American Mathematical Society, Providence, RI, 1999. MR1687388 (2000a:57089) Zbl 0935.57003