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An induction theorem for equivariant surgery. G-surgery. III. (English) Zbl 0535.57020

The paper is a continuation of the authors’ earlier work [Mem. Am. Math. Soc. 260 (1982; Zbl 0495.57014)] where the basic surgery theory for the construction of G-manifolds with a given ordinary homotopy type was developed. In this paper the authors prove an induction theorem for their surgery obstruction groups which is basic for the main applications of the theory. The induction theorem is a geometric theorem concerned with odd order nilpotent groups and states that certain prenormal maps (in their terminology) are prenormally cobordant to a pseudo-equivalence relative boundary. An exact statement of the main result needs unfortunately several pages of notations and definitions.
Reviewer: T.tom Dieck

MSC:

57S17 Finite transformation groups
57R67 Surgery obstructions, Wall groups
18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects)
57R65 Surgery and handlebodies

Citations:

Zbl 0495.57014
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