Coincidence theory for manifolds with boundary (Q1191871)

Let \(M\) and \(N\) be compact, connected, oriented manifolds of the same dimension with boundaries \(\partial M\), \(\partial N\), respectively. Let \(F,G:M\to N\) be maps such that \(G(\partial M)\subseteq\partial N\). If the Lefschetz number, \(\Lambda(F,G)\), defined by the author, is nonzero, then \(F\) and \(G\) have a coincidence point. When both maps preserve boundary points, the author obtains, for a class of differentiable maps, a formula for the algebraic number of coincidences which lie in the interior of \(M\).