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{1288703104,
author = {ASADI-GOLMANKHANEH, Mohammad A.},
title = {Double point of self-transverse immersions of M<sup>2n</sup> },
journal = {J. Math. Soc. Japan},
volume = {62},
number = {1},
year = {2010},
pages = { 1257-1271},
language = {en},
url = {http://dml.mathdoc.fr/item/1288703104}
}
ASADI-GOLMANKHANEH, Mohammad A. Double point of self-transverse immersions of M2n . J. Math. Soc. Japan, Tome 62 (2010) no. 1, pp. 1257-1271. http://gdmltest.u-ga.fr/item/1288703104/