Geodesic
Maps into the torus and minimal coincidence sets for homotopies
D. L. Goncalves 1   ; M. R. Kelly 2
1 Departamento de Matemática – IME-USP Caixa Postal 66281 – Ag. Cidade de São Paulo CEP: 05315-970 São Paulo, SP Brazil
2 Department of Mathematics and Computer Science Loyola University 6363 St Charles Avenue New Orleans, LA 70118, U.S.A.
Fundamenta Mathematicae, Tome 172 (2002) no. 2, pp. 99-106 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

Let $X,Y$ be manifolds of the same dimension. Given continuous mappings $f_i,g_i :X\to Y$, $i=0,1$, we consider the $1$-parameter coincidence problem of finding homotopies $f_t,g_t$, $0\leq t\leq 1$, such that the number of coincidence points for the pair $f_t,g_t$ is independent of $t$. When $Y$ is the torus and $f_0,g_0$ are coincidence free we produce coincidence free pairs $f_1,g_1$ 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.
DOI : 10.4064/fm172-2-1
Keywords: manifolds dimension given continuous mappings i consider parameter coincidence problem finding homotopies t leq leq number coincidence points pair t independent torus coincidence produce coincidence pairs homotopy joining coincidence each level torus characterize solution problem terms lefschetz coincidence number

D. L. Goncalves  1   ; M. R. Kelly  2

1 Departamento de Matemática – IME-USP Caixa Postal 66281 – Ag. Cidade de São Paulo CEP: 05315-970 São Paulo, SP Brazil
2 Department of Mathematics and Computer Science Loyola University 6363 St Charles Avenue New Orleans, LA 70118, U.S.A. 
@article{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},
     pages = {99--106},
     year = {2002},
     volume = {172},
     number = {2},
     doi = {10.4064/fm172-2-1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm172-2-1/}
}
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
SP  - 99
EP  - 106
VL  - 172
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4064/fm172-2-1/
DO  - 10.4064/fm172-2-1
LA  - en
ID  - 10_4064_fm172_2_1
ER  - 
%0 Journal Article
%A D. L. Goncalves
%A M. R. Kelly
%T Maps into the torus and
minimal coincidence sets for homotopies
%J Fundamenta Mathematicae
%D 2002
%P 99-106
%V 172
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4064/fm172-2-1/
%R 10.4064/fm172-2-1
%G en
%F 10_4064_fm172_2_1
D. L. Goncalves; M. R. Kelly. Maps into the torus and
minimal coincidence sets for homotopies. Fundamenta Mathematicae, Tome 172 (2002) no. 2, pp. 99-106. doi: 10.4064/fm172-2-1

Cité par Sources :