Publication Date

5-2014

Date of Final Oral Examination (Defense)

3-13-2014

Type of Culminating Activity

Thesis - Boise State University Access Only

Degree Title

Master of Science in Mathematics

Department

Mathematics

Major Advisor

Jens Harlander

Abstract

There are various ways one can try to extend the notion of a tree to higher dimensional cell complexes. Perhaps the most direct approach is via the notion of diagrammatic reducibility. In two dimensions, diagrammatic reducibility implies asphericity. The converse, however, is false. Even so, there exist simple, yet powerful tests for diagrammatic reducibility. One such test, S. M. Gersten’s Weight Test, is based on the Gauss-Bonnet Theorem.

In 1987, Gersten published a paper titled Branched Coverings of 2-Complexes and Diagrammatic Reducibility [1] that utilizes both branched covering spaces and the Weight Test to produce diagrammatically reducible 2-complexes. In this thesis, we rework Gersten’s paper and provide not only additional examples, but also details to important results from J. R. Stallings [7] and from M. Hall [3].

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