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On the classification of G-spheres. I. Equivariant transversality. (English) Zbl 0656.57024

This paper is the first in a series of three intended to study locally linear group actions on spheres for odd order groups. This first paper is devoted to the topic of equivariant transversality in the category of locally linear PL or topological manifolds. The approach to transversality is through the theory of equivariant submersions. The main results are a stable G-transversality theorem for the PL case, with gap hypotheses and an obstruction theory in the topological case. A major point is that the results are significantly different from the smooth case.
Reviewer: R.E.Stong

MSC:

57S17 Finite transformation groups
57Q65 General position and transversality
57N75 General position and transversality
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