Anosov theorem for coincidences on nilmanifolds

Seung Won Kim, and Jong Bum Lee. "Anosov theorem for coincidences on nilmanifolds." Fundamenta Mathematicae 185.3 (2005): 247-259. <http://eudml.org/doc/282817>.

@article{SeungWonKim2005,
abstract = {Suppose that L, L’ are simply connected nilpotent Lie groups such that the groups $γ_i(L)$ and $γ_i(L^\{\prime \})$ 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 , ’ of L, L’ induced by f,g.},
author = {Seung Won Kim, Jong Bum Lee},
journal = {Fundamenta Mathematicae},
keywords = {nilmanifold; Lefschetz coincidence number; Nielsen coincidence number},
language = {eng},
number = {3},
pages = {247-259},
title = {Anosov theorem for coincidences on nilmanifolds},
url = {http://eudml.org/doc/282817},
volume = {185},
year = {2005},
}

TY - JOUR
AU - Seung Won Kim
AU - Jong Bum Lee
TI - Anosov theorem for coincidences on nilmanifolds
JO - Fundamenta Mathematicae
PY - 2005
VL - 185
IS - 3
SP - 247
EP - 259
AB - Suppose that L, L’ are simply connected nilpotent Lie groups such that the groups $γ_i(L)$ and $γ_i(L^{\prime })$ 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 , ’ of L, L’ induced by f,g.
LA - eng
KW - nilmanifold; Lefschetz coincidence number; Nielsen coincidence number
UR - http://eudml.org/doc/282817
ER -