Abstract
AbstractIn this paper we study the averaging formula for Nielsen coincidence numbers of pairs of maps(f,g): M→Nbetween closed smooth manifolds of the same dimension. Suppose that G is a normal subgroup of Π = π1(M) with finite index andHis a normal subgroup of Δ = π1(N) with finite index such thatThen we investigate the conditions for which the following averaging formula holdswhereis any pair of fixed liftings of (f, g). We prove that the averaging formula holds whenMandNare orientable infra-nilmanifolds of the same dimension, and whenM = Nis a non-orientable infra-nilmanifold with holonomy groupℤ2and (f, g) admits a pair of liftingson the nil-coveringofM.
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