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Anosov theorem for coincidences on nilmanifolds

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Kim S., Lee J.

Fundamenta Mathematicae

2005

tom 185

nr 3

247-259

Suppose that L, L' are simply connected nilpotent Lie groups such that the groups $γ_i(L)$ and $γ_i(L')$ in their lower central series have the same dimension. We show that the Nielsen and Lefschetz coincidence numbers of maps f,g: Γ∖L → Γ'∖L' between nilmanifolds Γ∖L and Γ'∖L' can be computed algebraically as follows: L(f,g) = det(G⁎ - F⁎), N(f,g) = |L(f,g)|, where F⁎, G⁎ are the matrices, with respect to any preferred bases on the uniform lattices Γ and Γ', of the homomorphisms between the Lie algebras 𝔏, 𝔏' of L, L' induced by f,g.

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1 Fundamenta Mathematicae

1 Kim S.

1 Lee J.

1 2005

Wyniki wyszukiwania

Anosov theorem for coincidences on nilmanifolds