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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].
Recommended Citation
Allyn, Tyler, "Diagrammatically Reducible 2-Complexes" (2014). Boise State University Theses and Dissertations. 815.
https://scholarworks.boisestate.edu/td/815