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http://dx.doi.org/10.5831/HMJ.2010.32.1.141

COMMUTATIVE MONOID OF THE SET OF k-ISOMORPHISM CLASSES OF SIMPLE CLOSED k-SURFACES IN Z3  

Han, Sang-Eon (Faculty of Liberal Education, Institute of Pure and Applied Mathematics, Chonbuk National University)
Publication Information
Honam Mathematical Journal / v.32, no.1, 2010 , pp. 141-155 More about this Journal
Abstract
In this paper we prove that with some hypothesis the set of k-isomorphism classes of simple closed k-surfaces in ${\mathbf{Z}}^3$ forms a commutative monoid with an operation derived from a digital connected sum, k ${\in}$ {18,26}. Besides, with some hypothesis the set of k-homotopy equivalence classes of closed k-surfaces in ${\mathbf{Z}}^3$ is also proved to be a commutative monoid with the above operation, k ${\in}$ {18,26}.
Keywords
digital k-graph; digital k-surface; $(k_0,k_1)$-isomorphism; digital connected sum k-homotopy equivalence; k-contractibility; simple closed k-surface; (commutative) monoid;
Citations & Related Records
Times Cited By KSCI : 6  (Citation Analysis)
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