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

• Journal title : Honam Mathematical Journal
• Volume 32, Issue 1,  2010, pp.141-155
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2010.32.1.141
Title & Authors
COMMUTATIVE MONOID OF THE SET OF k-ISOMORPHISM CLASSES OF SIMPLE CLOSED k-SURFACES IN Z3
Han, Sang-Eon;

Abstract
In this paper we prove that with some hypothesis the set of k-isomorphism classes of simple closed k-surfaces in $\small{{\mathbf{Z}}^3}$ forms a commutative monoid with an operation derived from a digital connected sum, k $\small{{\in}}$ {18,26}. Besides, with some hypothesis the set of k-homotopy equivalence classes of closed k-surfaces in $\small{{\mathbf{Z}}^3}$ is also proved to be a commutative monoid with the above operation, k $\small{{\in}}$ {18,26}.
Keywords
digital k-graph;digital k-surface;$\small{(k_0,k_1)}$-isomorphism;digital connected sum k-homotopy equivalence;k-contractibility;simple closed k-surface;(commutative) monoid;
Language
English
Cited by
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