Algebraic & Geometric Topology

The cobordism class of the multiple points of immersions

Gábor Braun

Full-text: Open access

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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796823

Digital Object Identifier
doi:10.2140/agt.2008.8.581

Mathematical Reviews number (MathSciNet)
MR2443239

Zentralblatt MATH identifier
1145.57025

Subjects
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]

Keywords
multiple point manifold characteristic class generating function

Citation

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. https://projecteuclid.org/euclid.agt/1513796823


Export citation

References

  • F Hirzebruch, Topological methods in algebraic geometry, Classics in Math., Springer, Berlin (1995) Translated from the German and Appendix One by R L E Schwarzenberger, with a preface to the third English edition by the author and Schwarzenberger, Appendix Two by A Borel; Reprint of the 1978 edition
  • F Ronga, On multiple points of smooth immersions, Comment. Math. Helv. 55 (1980) 521–527
  • A Sz\Hucs, On the multiple points of immersions in Euclidean spaces, Proc. Amer. Math. Soc. 126 (1998) 1873–1882