Logging road construction in the coastal regions of British Columbia has always been a difficult and expensive undertaking. The soils are generally ill-suited to road construction, rock outcrops are numerous, and climatic conditions unfavourable. In
addition, the mineral soils are overlaid by a heavy layer of partly decomposed organic material....
In 1941, J.H.C. Whitehead posed the question of whether asphericity is a hereditary property for 2-dimensional CW complexes. This question remains unanswered, but has led to the development of several algebraic and topological properties that are sufficient (but not necessary) for the asphericity of presentation 2-complexes. While many of the...
Let H be a cyclically-presented group on n generators with a single defining relator. Attempts have been made to classify such groups by their order, their status as a 3-manifold group, and the asphericity status of their presentations. For groups with a defining relator of length 3 these classifications are...
We present a method by which torsion-free groups of automorphisms of a 2-dimensional hyperbolic building which act simply transitively on the vertex set can be constructed, and prove that any such group can be obtained by this construction. The method produces groups defined by finite presentations with strong small cancellation...
In 2014, W. Bogley identified a relation between the algebraic and geometric prop- erties of cyclically presented groups Gn (w) in the case where w = x0xkxl is a positive word of length three. Specifically, it was shown that the dynamics of the shift θG on the group G =...
This dissertation investigates the structure and topological properties of cyclicallypresented groups. First, a family of groups called groups of type Z is considered. Withfew exceptions, the finiteness, asphericity, fixed point, and 3-manifold spine problemsare solved. Most groups of type Z have a central element of infinite order fixed by theshift....
The Alexander polynomial is a well understood classical knot invariant with interesting symmetry properties and recent applications in knot Floer homology. There are many different ways to compute the Alexander polynomial, some involving algebraic techniques and others more geometric or combinatorial approaches. This is an interesting example of how different...
Winter wheat is commonly grown in dryland cropping systems in the Pacific Northwest region of semi-arid eastern Oregon. For agronomic, economic, and environmental reasons, it is important to understand the long-term sustainability of such dryland systems. The objective of this study was to evaluate the long-term effects of tillage, nitrogen...
