Higher Topological Complexity Number Of Digital Images
Project no. 21123 · Status: Kapanmış · 2020
Summary
<p>The main subject of this project is to deal with the calculation of higher topological complexity numbers in all aspects on digital images and reveal the similar and different aspects of the previously obtained results in topological spaces for the digital ground. For example, it is shown that the method of cohomological cup-product, that uses for TC calculation in topological spaces, does not work on digital images. An easier computation method for digital higher topological complexity numbers by constructing a topological group structure for digital images is presented via the concept of digital Lusternik-Schnirelmann category. It is tried to classify some finite digital spaces according to the (higher) topological complexity computation in one and two dimensional digital images. Just as with topological spaces, the digital topological complexity computation problem for a digital image is extended to a digital topological complexity computation problem for a function defined between digital images. Moreover, the point of view that provides the most general solution to the problem of calculating the higher topological complexity of a topological space and the method of calculating the higher topological complexity number for a fibration are presented. This is so valuable because it shows that it is possible to obtain results in topological spaces based on the studies done on digital images. </p>