Abstract
In classical fixed point and coincidence theory, the notion of
Nielsen numbers has proved to be extremely fruitful. Here we
extend it to pairs (f1,f2) of maps between manifolds of
arbitrary dimensions. This leads to estimates of the minimum
numbers MCC (f1,f2) (and MC (f1,f2), resp.) of path components (and of points, resp.) in the coincidence sets of those pairs of maps which are (f1,f2). Furthermore we deduce finiteness conditions for MC
(f1,f2). As an application, we compute both minimum numbers
explicitly in four concrete geometric sample situations. The
Nielsen decomposition of a coincidence set is induced by the
decomposition of a certain path space E(f1,f2) into path components. Its higher-dimensional topology captures further
crucial geometric coincidence data. An analoguous approach can be
used to define also Nielsen numbers of certain link maps.