Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X38420121215Multiple point of self-transverse immesions of certain manifolds869882292ENMohammad AliAsadi-GolmankhanehAssistant Prof. Mathematics Department, Urmia UniversityJournal Article20090827In this paper we will determine the multiple point manifolds of <br />certain self-transverse immersions in Euclidean spaces. Following <br />the triple points, these immersions have a double point <br />self-intersection set which is the image of an immersion of a smooth <br />5-dimensional manifold, cobordant to Dold manifold $V^5$ or a <br />boundary. We will show there is an immersion of $S^7times P^2$ in <br />$mathbb{R}^{13}$ with double point manifold cobordant to Dold <br />manifold $V^5$, and an immersion of $P^2times P^2times P^2times <br />P^2times P^2$ in $mathbb{R}^{15}$ with double point manifold a <br />boundary and the triple point set is odd number. These will be done <br />by introducing the product technique and reading off the <br />Stiefel-Whitney numbers of the self-intersection manifolds.http://bims.iranjournals.ir/article_292_f640c8c7d63984f075314fc293f12751.pdf