Balanced Folding Over a Polygon and Euler Numbers
EL-Kholy E* and El-Sharkawey E
Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt
- *Corresponding Author:
- EL-Kholy E
Department of Mathematics
Faculty of Science
E-mail: [email protected]
Received Date: March 23, 2016; Accepted Date: April 06, 2016; Published Date: April 12, 2016
Citation: EL-Kholy E, El-Sharkawey E (2016) Balanced Folding Over a Polygon and Euler Numbers. J Appl Computat Math 5:296. doi:10.4172/2168-9679.1000296
Copyright: © 2016 EL-Kholy E, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
In this paper we introduced a new folding over a polygon we called it balanced folding, then we proved that for a balanced folding of a simply connected surface M there is a subgroup of the group of all homeomorphisms of M that acts 1-transitively on the 2-cells of M. Also we explored the relationship between balanced folding and covering spaces. Finally we obtained a general relation of the Euler number of surfaces which may balance folded over a polygon and we also listed all the possibilities if M is a sphere balanced folded over a triangle and we gave the subgroup mentioned above in each case.