On the basis of the
Generalized Pontryagin-Thom construction (see Rimanyi & Szucs, 1998) and its
application in computing Thom polynomials (see Rimanyi, 2001) here we introduce a
new point of view in multiple-point theory. Using this approach we will
first show how to reprove results of Kleiman and his followers (the corank 1
case) then we will prove some new multiple-point formulas which are not
subject to the condition of corank ≤ 1. We will concentrate on the case of
complex analytic maps N∗→P∗+1, since this was the setting where the most
formulas were known before. The scheme of the computation is similar to the
one we used in computing Thom polynomials (see Rimanyi, 2001), with
an essential difference that here we need to compute nontrivial incidenceclasses.
