Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 62, Number 4 (2010), 1257-1271.
Double point of self-transverse immersions of M2n R4n-5
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.
J. Math. Soc. Japan, Volume 62, Number 4 (2010), 1257-1271.
First available in Project Euclid: 2 November 2010
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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