STABILIZERS OF FIXED POINT CLASSES AND NIELSEN NUMBERS OF n-VALUED MAPS
نویسندگان
چکیده
The stabilizer of a fixed point class of a map is the fixed subgroup of the induced fundamental group homomorphism based at a point in the class. A theorem of Jiang, Wang and Zhang is used to prove that if a map of a graph satisfies a strong remnant condition, then the stabilizers of all its fixed point classes are trivial. Consequently, if φp,f is the nvalued lift to a covering space p of a map f with strong remnant of a graph, then the Nielsen numbers are related by the equation N(φp,f ) = n ·N(f). Additional information concerning Nielsen numbers is obtained for n-valued lifts of maps of graphs with positive Lefschetz numbers and of maps of spaces with abelian fundamental groups and for extensions of n-valued maps. Subject Classification 55M20, 54C60
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