Dovermann, Karl Heinz; Petrie, Ted An induction theorem for equivariant surgery. G-surgery. III. (English) Zbl 0535.57020 Am. J. Math. 105, 1369-1403 (1983). 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 Cited in 1 ReviewCited in 6 Documents MSC: 57S17 Finite transformation groups 57R67 Surgery obstructions, Wall groups 18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects) 57R65 Surgery and handlebodies Keywords:induction theorem for their surgery obstruction groups; odd order nilpotent groups Citations:Zbl 0495.57014 PDFBibTeX XMLCite \textit{K. H. Dovermann} and \textit{T. Petrie}, Am. J. Math. 105, 1369--1403 (1983; Zbl 0535.57020) Full Text: DOI