Thesis in combinatorial group theory.

Complexes of groups are higher dimensional analogs of graphs of groups. The Bass-Serre theory of groups acting on trees is generalized (to the extent that is possible) to this higher dimensional setting. The complexes of groups that arise from group actions are called good. Simple examples are presented to show that not all complexes of groups are good. A sufficient condition for a 2-complex of groups to be good is given. The condition is a generalized small cancellation condition, that is, a "combinatorial non-positive curvature" condition. Small cancellation hypotheses are formulated in terms of conformal structures on 2-complexes. With this approach, Lyndon's curvature formula takes on a more geometric appearance. Then diagrammatic methods, typical of small cancellation theory, are utilized. Groups arising as the amalgamated sum of an assemblage are studied. This is a construction extending the free product with amalgamation construction. A basic problem is to determine whether or not a given assemblage collapses in the direct limit. A sufficient condition is given to ensure no collapsing occurs. Coxeter groups are well known examples of groups with the structure as assemblages. The notion of a Coxeter complex is extended to the situation of an assemblage and is shown to be contractible in certain cases.PhDMathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/103361/1/9034407.pdfDescription of 9034407.pdf : Restricted to UM users only