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Algebraic Invariants in Abstract Cellular Complex

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Abstract

Kovalevsky has developed an abstract cellular complex for representing digital images in the combinatorial grid. This paper initiates the notions of cellular homotopy and cellular path homotopy through the continuous connected preserving map and investigates some of their basic properties in the abstract cellular complex. Further, the concept of fundamental groups in the abstract cellular complex is introduced using the notion of cellular homotopy and some of their basic properties are investigated. Finally, the paper presents the concept of homology and fixed point property in the connected abstract cellular complex.

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Both authors contributed equally.

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  1. Department of Applied Mathematics and Computational Sciences, PSG College of Technology, Coimbatore, 641 004, India

    G. Sai Sundara Krishnan & R. Syama

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  1. G. Sai Sundara Krishnan
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  2. R. Syama
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Correspondence to R. Syama.

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Krishnan, G.S.S., Syama, R. Algebraic Invariants in Abstract Cellular Complex. Results Math 76, 150 (2021). https://doi.org/10.1007/s00025-021-01455-w

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