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- W3204106098 abstract "In this paper we prove results relating to two homotopy relations and four homology theories developed in the topology of digital images.<br /><br />We introduce a new type of homotopy relation for digitally continuous functions which we call ``strong homotopy.'' Both digital homotopy and strong homotopy are natural digitizations of classical topological homotopy: the difference between them is analogous to the difference between digital 4-adjacency and 8-adjacency in the plane.<br /><br />We also consider four different digital homology theories: a simplicial homology theory by Arslan et al which is the homology of the clique complex, a singular simplicial homology theory by D. W. Lee, a cubical homology theory by Jamil and Ali, and a new kind of cubical homology for digital images with $c_1$-adjacency which is easily computed, and generalizes a construction by Karaca & Ege. We show that the two simplicial homology theories are isomorphic to each other, but distinct from the two cubical theories.<br /><br />We also show that homotopic maps have the same induced homomorphisms in the cubical homology theory, and strong homotopic maps additionally have the same induced homomorphisms in the simplicial theory." @default.
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- W3204106098 date "2021-10-01" @default.
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- W3204106098 title "Digital homotopy relations and digital homology theories" @default.
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- W3204106098 doi "https://doi.org/10.4995/agt.2021.13154" @default.
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