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Maps into the torus and minimal coincidence sets for homotopies

D. L. GoncalvesM. R. Kelly — 2002

Fundamenta Mathematicae

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...

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