Fixed Point Sets of Fiber-preserving Maps
نویسندگان
چکیده
Let F = (E, p, B;Y ) be a fiber bundle where E, B and Y are connected finite polyhedra. Let f : E → E be a fiber-preserving map and A ⊆ E a closed, locally contractible subset. We present necessary and sufficient conditions for A and its subsets to be the fixed point sets of maps fiber-homotopic to f . The necessary conditions correspond to those introduced by Schirmer in 1990 but, in the fiber-preserving setting, homotopies are fiber-preserving. Those conditions are shown to be sufficient in the presence of additional hypotheses on the bundle and on the map f . The hypotheses can be weakened in the case that f is fiber homotopic to the identity. Subject Classification 55M20; 55R10
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