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Maps into the torus and minimal coincidence sets for homotopies

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Goncalves D., Kelly M.

Fundamenta Mathematicae

2002

tom 172

nr 2

99-106

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.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Goncalves D.

1 Kelly M.

1 2002

Wyniki wyszukiwania

Maps into the torus and minimal coincidence sets for homotopies