1Departamento de Matemática – IME-USP Caixa Postal 66281 – Ag. Cidade de São Paulo CEP: 05315-970 São Paulo, SP Brazil 2Department 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
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.
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
Affiliations des auteurs :
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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author = {D. L. Goncalves and M. R. Kelly},
title = {Maps into the torus and
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minimal coincidence sets for homotopies
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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
