Bordism classes of the multiple points manifolds

Details Bordism classes of the multiple points manifolds Bordism classes of the multiple points manifolds

2000-08-07

arxiv.org/abs/math/0008049v1

Mathematics

Geometric Topology

5 pages, AmSLaTeX

Scientific paper

Let $f:V^n\looparrowright M^m$ 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.

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