IJPAM: Volume 22, No. 4 (2005)

THE FUNDAMENTAL GROUP OF THE CONNECTED SUM
OF MANIFOLDS AND THEIR FOLDINGS

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


Abstract.In this paper, we will introduce the folding on the connected sum of some types of manifolds which are determined by their fundamental group. Also, the fundamental group of the unfolding of the connected sum will be deduced. Some types of conditional foldings restricted on the elements of the fundamental groups are deduced. Theorems governing these relations will be achieved. Some applications in manufacturing are presented.

Received: July 11, 2005

AMS Subject Classification: 51H10, 57N10

Key Words and Phrases: manifolds, folding, connected sum, fundamental group

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 22
Issue: 4