Suppose that L, L’ are simply connected nilpotent Lie groups such that the groups and 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm185-3-3,
author = {Seung Won Kim and Jong Bum Lee},
title = {Anosov theorem for coincidences on nilmanifolds},
journal = {Fundamenta Mathematicae},
volume = {185},
year = {2005},
pages = {247-259},
zbl = {1079.55008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm185-3-3}
}
Seung Won Kim; Jong Bum Lee. Anosov theorem for coincidences on nilmanifolds. Fundamenta Mathematicae, Tome 185 (2005) pp. 247-259. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm185-3-3/