Multiple points of immersions

Abstract

Given smooth manifolds $V^n$ and $M^m$, an integer $k$, and an immersion $f:V\looparrowright M$, we have constructed an obstruction for existence of regular homotopy of $f$ to an immersion $f^{\prime }:V\looparrowright M$ without $k$-fold points. This obstruction takes values in certain framed bordism group, and for $(k+1)(n+1)\le km$ turns out to be complete.

Minor corrections