Algebraic & Geometric Topology

The cobordism class of the multiple points of immersions

Gábor Braun

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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.

Article information

Algebr. Geom. Topol., Volume 8, Number 1 (2008), 581-601.

Received: 27 June 2005
Revised: 19 April 2006
First available in Project Euclid: 20 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R20: Characteristic classes and numbers 57R42: Immersions
Secondary: 57R75: O- and SO-cobordism 16W60: Valuations, completions, formal power series and related constructions [See also 13Jxx]

multiple point manifold characteristic class generating function


Braun, Gábor. The cobordism class of the multiple points of immersions. Algebr. Geom. Topol. 8 (2008), no. 1, 581--601. doi:10.2140/agt.2008.8.581.

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