Nielsen type invariants and the location, of coincidence sets in positive codimension

摘要

Let two mappings f, g be given between smooth manifolds M, N of different dimensions n + m and n, respectively. We consider the problem of the coincidence set Coin(f, g) minimization. Suppose the set Coin(f, g) is equal to a finite union of preimages (under f × g) of diagonal points of the target space N squared, and each preimage is a closed m-submanifold in M. The minimizing coincidence problem may, then, be considered with respect to those preimages. How to coalesce two of them, to move or to remove one of them via homotopies of the mappings f, g? In this paper we give constructive answers to those questions, under additional conditions.