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Creators/Authors contains: "Cappell, Sylvain"

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  1. ; ; (, Proceedings of the Royal Society of Edinburgh: Section A Mathematics)
    For a finite group$$G$$of not prime power order, Oliver showed that the obstruction for a finite CW-complex$$F$$to be the fixed point set of a contractible finite$$G$$-CW-complex is determined by the Euler characteristic$$\chi (F)$$. (He also has similar results for compact Lie group actions.) We show that the analogous problem for$$F$$to be the fixed point set of a finite$$G$$-CW-complex of some given homotopy type is still determined by the Euler characteristic. Using trace maps on$$K_0$$[2, 7, 18], we also see that there are interesting roles for the fundamental group and the component structure of the fixed point set. 
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  2. ; ; (, Proceedings of the Royal Society of Edinburgh: Section A Mathematics)
    Smith theory says that the fixed point set of a semi-free action of a group$$G$$on a contractible space is$${\mathbb {Z}}_p$$-acyclic for any prime factor$$p$$of the order of$$G$$. Jones proved the converse of Smith theory for the case$$G$$is a cyclic group acting semi-freely on contractible, finite CW-complexes. We extend the theory to semi-free group actions on finite CW-complexes of given homotopy types, in various settings. In particular, the converse of Smith theory holds if and only if a certain$$K$$-theoretical obstruction vanishes. We also give some examples that show the geometrical effects of different types of$$K$$-theoretical obstructions. 
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  3. ; ; (, Advances in Mathematics)
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