Nielsen Number of a Covering Map
نویسنده
چکیده
Is it possible to find a formula expressing the Nielsen number N( f ) by the numbers N( ̃ f ) where ̃ f runs the set of all lifts? Such a formula seems very desirable since the difficulty of computing the Nielsen number often depends on the size of the fundamental group. Since π1 ̃ X ⊂ π1X , the computation of N( ̃ f ) may be simpler. We will translate this problem to algebra. The main result of the paper is Theorem 4.2 expressing N( f ) as a linear combination of {N( ̃ fi)}, where the lifts are representing all the H-Reidemeister classes of f . The discussed problem is analogous to the question about “the Nielsen number product formula” raised by Brown in 1967 [1]. A locally trivial fibre bundle p : E → B and a
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