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Nielsen theory of transversal fixed point sets (with an appendix: C and C0 fixed point sets are the same, by R. E. Greene)

Helga Schirmer — 1992

Fundamenta Mathematicae

Examples exist of smooth maps on the boundary of a smooth manifold M which allow continuous extensions over M without fixed points but no such smooth extensions. Such maps are studied here in more detail. They have a minimal fixed point set when all transversally fixed maps in their homotopy class are considered. Therefore we introduce a Nielsen fixed point theory for transversally fixed maps on smooth manifolds without or with boundary, and use it to calculate the minimum number of fixed points...

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