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Multiplicative Property of the Digital Fundamental Group

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Abstract

Recent papers have partially discussed the multiplicative or the non-multiplicative property of the digital fundamental group. Thus, the paper studies a condition of which the multiplicative property of the digital fundamental group holds. Precisely, for two digital spaces with k i -adjacencies of \(\mathbf{Z}^{n_{i}}\) , denoted by (X i ,k i ), i∈{1,2}, using the L HS- or L HC-property of the digital product (or Cartesian product of digital spaces) with k-adjacency (X 1×X 2,k), a k-homotopic thinning of the digital product, and various properties from digital covering and digital homotopy theories, we provide a method of calculating the k-fundamental group of the digital product. Furthermore, the notion of HT-(k 0,k 1)-isomorphism is established and used in calculating the k-fundamental group of a digital product. Finally, we find a condition of which the multiplicative property of the digital fundamental group holds. This property can be used in classifying digital spaces from the view points of digital homotopy theory, mathematical morphology, and digital geometry.

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Authors and Affiliations

  1. Faculty of Liberal Education, Institute of Pure and Applied Mathematics, Chonbuk National University, Jeonju-City Jeonbuk, 561-756, Republic of Korea

    Sang-Eon Han

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  1. Sang-Eon Han
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Correspondence to Sang-Eon Han.

Additional information

This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion Fund) (KRF-2008-313-C00119).

This paper was supported by the selection of research-oriented professor of Chonbuk National University in 2009.

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Han, SE. Multiplicative Property of the Digital Fundamental Group. Acta Appl Math 110, 921–944 (2010). https://doi.org/10.1007/s10440-009-9486-5

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  • DOI: https://doi.org/10.1007/s10440-009-9486-5

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