Anosov theorem for coincidences on nilmanifolds

• Autorzy: Seung Won Kim , Jong Bum Lee
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 55M20: Fixed points and coincidences
• 57S30: Discontinuous groups of transformations
• 54H25: Fixed-point and coincidence theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2005
• Tom: 185
• Numer: 3
• Strony: 247-259

Daty

wydano

2005

Twórcy

autor

Seung Won Kim

• Department of Mathematics, Sogang University, Seoul 121-742, Korea

autor

Jong Bum Lee

• Department of Mathematics, Sogang University, Seoul 121-742, Korea

Identyfikatory

DOI

10.4064/fm185-3-3