# Multiple point of self-transverse immesions of certain manifolds

Document Type : Research Paper

Author

Assistant Prof. Mathematics Department, Urmia University

Abstract

In this paper we will determine the multiple point manifolds of
certain self-transverse immersions in Euclidean spaces. Following
the triple points, these immersions have a double point
self-intersection set which is the image of an immersion of a smooth
5-dimensional manifold, cobordant to Dold manifold $V^5$ or a
boundary. We will show there is an immersion of $S^7times P^2$ in
$mathbb{R}^{13}$ with double point manifold cobordant to Dold
manifold $V^5$, and an immersion of $P^2times P^2times P^2times P^2times P^2$ in $mathbb{R}^{15}$ with double point manifold a
boundary and the triple point set is odd number. These will be done
by introducing the product technique and reading off the
Stiefel-Whitney numbers of the self-intersection manifolds.

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Main Subjects

### History

• Receive Date: 27 August 2009
• Revise Date: 13 February 2011
• Accept Date: 13 February 2011
• First Publish Date: 15 December 2012