2019/05/29 by Krzyżanowska, Iwona, Nowel, Aleksandra
#14P25 57R45 12Y05 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1905.12284
The definition of the intersection number of a map with a closed manifold can be extended to the case of a closed stratified set such that the difference between dimensions of its two biggest strata is greater than 1. The set Sigma of matrices of positive corank is an example of such a set. It turns out that the intersection number of a map from an (n-k+1)--dimensional manifold with boundary into the set of (n x k) real matrices with Sigma coincides with a homotopy invariant associated with a map going to the Stiefel manifold. In a polynomial case, we present an effective method to compute this intersection number. We also show how to use it to count the number mod 2 or the algebraic sum of cross--cap singularities of a map from an m--dimensional manifold with boundary to R2m-1.