Volume 8, issue 1 (2008)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
The cobordism class of the multiple points of immersions

Gábor Braun

Algebraic & Geometric Topology 8 (2008) 581–601
Abstract

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.

Keywords
multiple point manifold, characteristic class, generating function
Mathematical Subject Classification 2000
Primary: 57R20, 57R42
Secondary: 57R75, 16W60
References
Publication
Received: 27 June 2005
Revised: 19 April 2006
Published: 12 May 2008
Authors
Gábor Braun
Alfréd Rényi Institute of Mathematics
Hungarian Academy of Sciences
Budapest
Reáltanoda u 13–15
1053
Hungary
http://www.renyi.hu/~braung/