Geodesic
The cobordism class of the multiple points of immersions
Braun, Gábor1
1Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Reáltanoda u 13–15, 1053, Hungary
Algebraic and Geometric Topology, Tome 8 (2008) no. 1, pp. 581-601
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Using generating functions, we derive a multiple point formula for every generic immersion between even dimensional oriented manifolds. This produces explicit formulas for the signature and Pontrjagin numbers of the multiple point manifolds. The formulas take a particular simple form in many special cases, eg when the immersion is nullhomotopic, we recover Szűcs’s formulas in [Proc. Amer. Math. Soc. 126 (1998) 1873-1882]. They also include Hirzebruch’s virtual signature formula in Topological methods in algebraic geometry.

DOI : 10.2140/agt.2008.8.581
Keywords: multiple point manifold, characteristic class, generating function

Braun, Gábor  1

1 Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Reáltanoda u 13–15, 1053, Hungary 
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Braun, Gábor. The cobordism class of the multiple points of immersions. Algebraic and Geometric Topology, Tome 8 (2008) no. 1, pp. 581-601. doi: 10.2140/agt.2008.8.581

[1] F Hirzebruch, Topological methods in algebraic geometry, Classics in Math., Springer (1995)

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

[3] A Szűcs, On the multiple points of immersions in Euclidean spaces, Proc. Amer. Math. Soc. 126 (1998) 1873

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