Abstract
In this paper we consider the 1-parameter coincidence problem of finding homotopies of pairs of maps (f t,g t) such that the number of coincidence points is independent of t. A number of results for the root problem ( g t constant) for maps between surfaces are given. Also, for the fixed point problem ( g t the identity) on the 2-sphere we obtain a negative result for every degree different from negative one. That is, the existence of pairs f 0 and f 1 each having one fixed point, but for some t, f t has additional fixed points.
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