ASPHERICITY OF MIXED MONOID PRESENTATIONS BY USING GENERALIZED WEIGHT TEST METHOD

TAY, CHOO CHUAN (2008) ASPHERICITY OF MIXED MONOID PRESENTATIONS BY USING GENERALIZED WEIGHT TEST METHOD. PhD thesis, Universiti Kebangsaan Malaysia.

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Abstract

Pictures over group presentation are the duals of Van Kampen diagrams, known widely in geometric group theory. They have proved to be effective tools in obtaining results concerning groups such as group presentations. Hence, pictures over monoid presentations are recently been considered. The sphericity of the mixed monoid presentations can be determined by these pictures. The theory concerning monoid presentations, monoid pictures, relative monoid presentation’s operations and its graphs, mixed monoid presentation's operations and its graphs and also the pictures of the mixed monoid presentations are reviewed. By generalizing Adjan’s cycle test and reorganizing Bogley and Pride relative test, a new test called generalized weight test is introduced in order to determine the asphericity of various class of mixed monoid presentations. In the method of generalized weight test, a mixed monoid presentation is said to be aspherical if the generalized left graph or the generalized right graph possess an asphericity weight function. The study is carried out to identify the general characteristics of an aspherical mixed monoid presentation, with a singleton set . This mixed monoid presentation contains words relation consisting of . The general characteristics of the spherical picture are shown. The results of sphericity of the mixed monoid presentations can be proved by pictures. These followed by the proving of asphericity of mixed monoid presentations through the generalized weight test which consists of one generator and one relator. Besides this, the mixed moniod presentations consisting of two generators and one or two relators are also being considered. Pictures will be used to prove the results of sphericity of the mixed monoid presentations. Whereas, the generalized weight test method is used to prove the asphericity of mixed monoid presentations.

Item Type: Thesis (PhD)
Subjects: Q Science > Q Science (General)
Divisions: Faculty of Electrical Engineering > Department of Control, Instrumentation & Automation
Depositing User: Choo Chuan Tay
Date Deposited: 15 Jan 2013 02:10
Last Modified: 28 May 2015 03:43
URI: http://eprints.utem.edu.my/id/eprint/6512
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