On the triple points of singular maps
Tobias Ekholm, András Szücs · Commentarii Mathematici Helvetici · 2002
The number of triple points (mod 2) of a self-transverse immersion of a closed 2nmanifold M into 3n-space are known to equal one of the Stiefel-Whitney numbers of M .This result is generalized to the case of generic (i.e.stable) maps with singularities.Besides triple points and Stiefel-Whitney numbers, a certain linking number of the manifold of singular values with the rest of the image is involved in the generalized equation which corrects an erroneous formula in [9].If n is even and the closed manifold is oriented then the equations mentioned above make sense over the integers.Together, the integer-and mod 2 generalized equations imply that a certain Stiefel-Whitney number of closed oriented 4k-manifolds vanishes.This Stiefel-Whitney number is in fact the first in a family which vanish on such manifolds.