The objective of this research work is to develop a better estimation or even calculate the exact Nielsen number of spaces such as compact polyhedra, manifolds, surfaces etc. We will do so by finding a new approach to existing techniques, in particular the mod H Nielsen theory technique, the q theory technique, the W-characteristic map technique etc. (see section below for more details). We furthermore hope to better determine the relationships between these techniques and improve upon them if possible. We will investigate the use of the open-source algebra software "GAP" (see www.gap-system.org) to help us with this research project. We also plan to develop an algorithm to estimate and/or calculate the Nielsen number. Moreover, we will try to find the link and the usage of Nielsen Theory with the Fixed Point Theory on Banach spaces, since there is a strong research group of analytic fixed point theorists in Thailand.
