Maps into the torus and minimal coincidence sets for homotopies

• Autorzy: D. L. Goncalves , M. R. Kelly
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 55M20: Fixed points and coincidences
• 57M05: Fundamental group, presentations, free differential calculus

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2002
• Tom: 172
• Numer: 2
• Strony: 99-106

Daty

wydano

2002

Twórcy

autor

D. L. Goncalves

• Departamento de Matemática - IME-USP, Caixa Postal 66281 - Ag. Cidade de São Paulo, CEP: 05315-970, São Paulo, SP Brazil

autor

M. R. Kelly

• Department of Mathematics, and Computer Science, Loyola University, 6363 St Charles Avenue, New Orleans, LA 70118, U.S.A.

Identyfikatory

DOI

10.4064/fm172-2-1