## Algebraic & Geometric Topology

### Singularities of projected immersions revisited

Gábor Lippner

#### Abstract

Szűcs proved [Bull. London Math. Soc. 32 (2000) 364-374] that the $r$–tuple-point manifold of a generic immersion is cobordant to the $Σ1r−1$–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

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

Dates
Revised: 19 February 2009
Accepted: 17 June 2009
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513797039

Digital Object Identifier
doi:10.2140/agt.2009.9.1623

Mathematical Reviews number (MathSciNet)
MR2539190

Zentralblatt MATH identifier
1177.57025

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

Keywords
immersion prim map multiple point

#### Citation

Lippner, Gábor. Singularities of projected immersions revisited. Algebr. Geom. Topol. 9 (2009), no. 3, 1623--1635. doi:10.2140/agt.2009.9.1623. https://projecteuclid.org/euclid.agt/1513797039

#### References

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