The higher topological complexity in digital images

Melih İs, Ismet Karaca

Abstract

Y. Rudyak develops the concept of the topological complexity TC(X) defined by M. Farber. We study this notion in digital images by using the fundamental properties of the digital homotopy. These properties can also be useful for the future works in some applications of algebraic topology besides topological robotics. Moreover, we show that the cohomological lower bounds for the digital topological complexity TC(X,κ) do not hold.

Keywords

topological complexity; digital topology; homotopy theory; digital topological complexity; image analysis

Subject classification

46M20; 68U05; 68U10; 68T40; 62H35

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References

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