Geodesic
Maps into the torus and minimal coincidence sets for homotopies
D. L. Goncalves1 ; M. R. Kelly2
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

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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. 
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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

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