Journal of the Mathematical Society of Japan

Double point of self-transverse immersions of M2n R4n-5

Mohammad A. ASADI-GOLMANKHANEH

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Abstract

A self-transverse immersion of a smooth manifold M2n in R4n-5 for n > 5 has a double point self-intersection set which is the image of an immersion of a smooth 5-dimensional manifold, cobordant to Dold manifold V5 or a boundary. We will show that the double point manifold of any such immersion is a boundary. The method of proof is to evaluate the Stiefel-Whitney numbers of the double point self-intersection manifold. By a certain method these numbers can be read off from spherical elements of H4n-5QMO(2n-5), corresponding to the immersions under the Pontrjagin-Thom construction.

Article information

Source
J. Math. Soc. Japan, Volume 62, Number 4 (2010), 1257-1271.

Dates
First available in Project Euclid: 2 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1288703104

Digital Object Identifier
doi:10.2969/jmsj/06241257

Mathematical Reviews number (MathSciNet)
MR2761896

Zentralblatt MATH identifier
1258.57014

Subjects
Primary: 57R42: Immersions
Secondary: 55R40: Homology of classifying spaces, characteristic classes [See also 57Txx, 57R20] 55Q25: Hopf invariants 57R75: O- and SO-cobordism

Keywords
immersion Hurewicz homomorphism spherical classes Stiefel-Whitney numbers

Citation

ASADI-GOLMANKHANEH, Mohammad A. Double point of self-transverse immersions of M 2 n ↬ R 4 n -5. J. Math. Soc. Japan 62 (2010), no. 4, 1257--1271. doi:10.2969/jmsj/06241257. https://projecteuclid.org/euclid.jmsj/1288703104


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