The cobordism class of the multiple points of immersions

Braun, Gábor

doi:10.2140/agt.2008.8.581

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The cobordism class of the multiple points of immersions

Gábor Braun

Algebraic & Geometric Topology 8 (2008) 581–601

DOI: 10.2140/agt.2008.8.581

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/

Volume 8, issue 1 (2008)