Multiple points of immersions

2002/03/13 by Konstantin Salikhov, Salikhov, Konstantin · 1 citation
Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GT

paper · pdf · doi:10.48550/arxiv.math/0203118

Minor corrections

openalex publication_date 2002/03/13 · arxiv created 2002/07/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given smooth manifolds Vⁿ 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':V\looparrowright M without k-fold points. This obstruction takes values in certain framed bordism group, and for (k+1)(n+1)≤ km turns out to be complete.

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