Let X,Y be manifolds of the same dimension. Given continuous mappings , i = 0,1, we consider the 1-parameter coincidence problem of finding homotopies , 0 ≤ t ≤ 1, such that the number of coincidence points for the pair is independent of t. When Y is the torus and f₀,g₀ are coincidence free we produce coincidence free pairs f₁,g₁ such that no homotopy joining them is coincidence free at each level. When X is also the torus we characterize the solution of the problem in terms of the Lefschetz coincidence number.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm172-2-1,
author = {D. L. Goncalves and M. R. Kelly},
title = {Maps into the torus and minimal coincidence sets for homotopies},
journal = {Fundamenta Mathematicae},
volume = {173},
year = {2002},
pages = {99-106},
zbl = {0988.55002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm172-2-1}
}
D. L. Goncalves; M. R. Kelly. Maps into the torus and minimal coincidence sets for homotopies. Fundamenta Mathematicae, Tome 173 (2002) pp. 99-106. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm172-2-1/