Bordism classes of the multiple points manifolds

Konstantin Salikhov

paper

Bordism classes of the multiple points manifolds

arXiv:math/0008049

Abstract

Let $f : V^{n} ↬ M^{m}$ be a smooth generic immersion. Then the set of points, that have at least $k$ preimages is an image of a (non-generic) immersion. If the manifolds $V^{n}$ and $M^{m}$ are oriented and $m - n$ is even, then the manifold of $k$ -fold points is also oriented. In this paper we compute the oriented bordism class of the manifold of $k$ -fold points in terms of the differential $df$ , provided the tangent bundle of the manifold $M^{m}$ has a nowhere zero cross-section.

5 pages, AmSLaTeX