Maps into the torus and minimal coincidence sets for homotopies

D. L. Goncalves, and M. R. Kelly. "Maps into the torus and minimal coincidence sets for homotopies." Fundamenta Mathematicae 172.2 (2002): 99-106. <http://eudml.org/doc/283264>.

@article{D2002,
abstract = {Let X,Y be manifolds of the same dimension. Given continuous mappings $f_i,g_i :X → Y$, i = 0,1, we consider the 1-parameter coincidence problem of finding homotopies $f_t,g_t$, 0 ≤ t ≤ 1, such that the number of coincidence points for the pair $f_t,g_t$ 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.},
author = {D. L. Goncalves, M. R. Kelly},
journal = {Fundamenta Mathematicae},
keywords = {coincidence point; root; torus},
language = {eng},
number = {2},
pages = {99-106},
title = {Maps into the torus and minimal coincidence sets for homotopies},
url = {http://eudml.org/doc/283264},
volume = {172},
year = {2002},
}

TY - JOUR
AU - D. L. Goncalves
AU - M. R. Kelly
TI - Maps into the torus and minimal coincidence sets for homotopies
JO - Fundamenta Mathematicae
PY - 2002
VL - 172
IS - 2
SP - 99
EP - 106
AB - Let X,Y be manifolds of the same dimension. Given continuous mappings $f_i,g_i :X → Y$, i = 0,1, we consider the 1-parameter coincidence problem of finding homotopies $f_t,g_t$, 0 ≤ t ≤ 1, such that the number of coincidence points for the pair $f_t,g_t$ 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.
LA - eng
KW - coincidence point; root; torus
UR - http://eudml.org/doc/283264
ER -