Algebraic & Geometric Topology

Singularities of projected immersions revisited

Gábor Lippner

Full-text: Open access


Szűcs proved [Bull. London Math. Soc. 32 (2000) 364-374] that the r–tuple-point manifold of a generic immersion is cobordant to the Σ1r1–point manifold of its generic projection. Here we extend this by showing that the natural mappings of these manifolds are bordant to each other. The main novelty of our approach is that we construct an explicit geometric realization of the bordism.

Article information

Algebr. Geom. Topol., Volume 9, Number 3 (2009), 1623-1635.

Received: 21 May 2008
Revised: 19 February 2009
Accepted: 17 June 2009
First available in Project Euclid: 20 December 2017

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R42: Immersions 57R45: Singularities of differentiable mappings

immersion prim map multiple point


Lippner, Gábor. Singularities of projected immersions revisited. Algebr. Geom. Topol. 9 (2009), no. 3, 1623--1635. doi:10.2140/agt.2009.9.1623.

Export citation


  • V I Arnold, V V Goryunov, O V Lyashko, V A Vasil$'$ev, Singularity theory. I, from: “Dynamical systems. VI”, Encyclopaedia Math. Sci. 6, Springer, Berlin (1993) iv+245 Translated from the 1988 Russian original by A Iacob
  • C McCrory, Cobordism operations and singularities of maps, Bull. Amer. Math. Soc. 82 (1976) 281–283
  • C McCrory, Geometric homology operations, from: “Studies in algebraic topology”, (G-C Rota, editor), Adv. in Math. Suppl. Stud. 5, Academic Press, New York (1979) 119–141
  • F Ronga, On multiple points of smooth immersions, Comment. Math. Helv. 55 (1980) 521–527
  • A Sz\Hucs, On the cobordism groups of immersions and embeddings, Math. Proc. Cambridge Philos. Soc. 109 (1991) 343–349
  • A Sz\Hucs, On the singularities of hyperplane projections of immersions, Bull. London Math. Soc. 32 (2000) 364–374