IJPAM: Volume 29, No. 3 (2006)

FOLDINGS AND RETRACTIONS OF MANIFOLDS
AND THEIR FUNDAMENTAL GROUPS

M. El-Ghoul$^1$, A.E. El-Ahmady$^2$, H. Rafat$^3$, M. Abu-Saleem$^4$
$^{1,2,3,4}$Department of Mathematics
Faculty of Science
Tanta University
Tanta, EGYPT
$^1$e-mail: m_elghoul2006@yahoo.com
$^4$e-mail: mohammedabusaleem2005@yahoo.com


Abstract.In this paper, we introduce the definition of the unfolding on the fundamental group. The folding on a wedge sum of some types of manifolds which are determined by their fundamental group are obtained. Some types of conditional foldings restricted on the elements of the fundamental groups are deduced. The effect of retraction of manifolds on the fundamental group is obtained. The folding of variation curvature of manifolds on their fundamental group are presented. Theorems governing these relations are achieved.

Received: May 17, 2006

AMS Subject Classification: 51H20, 57N10, 57M05, 14F35, 20F34

Key Words and Phrases: manifolds, folding, fundamental group

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 29
Issue: 3