Geodesic
Singularities of projected immersions revisited
Lippner, Gábor1
1Rényi Alfréd Institute of Mathematics, Budapest, Hungary
Algebraic and Geometric Topology, Tome 9 (2009) no. 3, pp. 1623-1635
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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.

DOI : 10.2140/agt.2009.9.1623
Keywords: immersion, prim map, multiple point

Lippner, Gábor  1

1 Rényi Alfréd Institute of Mathematics, Budapest, Hungary 
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Lippner, Gábor. Singularities of projected immersions revisited. Algebraic and Geometric Topology, Tome 9 (2009) no. 3, pp. 1623-1635. doi: 10.2140/agt.2009.9.1623

[1] 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 (1993)

[2] C Mccrory, Cobordism operations and singularities of maps, Bull. Amer. Math. Soc. 82 (1976) 281

[3] C Mccrory, Geometric homology operations, from: "Studies in algebraic topology" (editor G C Rota), Adv. in Math. Suppl. Stud. 5, Academic Press (1979) 119

[4] F Ronga, On multiple points of smooth immersions, Comment. Math. Helv. 55 (1980) 521

[5] A Szűcs, On the cobordism groups of immersions and embeddings, Math. Proc. Cambridge Philos. Soc. 109 (1991) 343

[6] A Szűcs, On the singularities of hyperplane projections of immersions, Bull. London Math. Soc. 32 (2000) 364

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