Classical and digital homotopy classes

Abstract

In this paper, we examine the relations between classical homotopy groups, digital fundamental groups of L. Boxer [6], and digital homotopy classes on the digital wedge products of pointed digital diamond (or square) circles. We demonstrate that the classical homotopy groups of pointed functions from a wedge product of homotopy simple closed curves to itself may differ completely from the digital homotopy monoids consisting of the classes of NPu pointed homotopic functions from the digital wedge product of pointed digital diamond (or square) circles to itself under the κ-adjacency relations on Z2 for κ=4,8 and u∈{1,2}.