Date of Award
Doctor of Philosophy
Chris Hruska, Boris Okun, Peter Hinow, Bruce Wade
3-manifold, group boundary, semidirect product, strongly polycyclic, Z-structure
Z-structures were originally formulated by Bestvina in order to axiomatize the properties that an ideal group boundary should have. In this dissertation, we prove that if a given group admits a Z-structure, then any semidirect product of that group with an infinite cyclic group will also admit a Z-structure. We then show how this can be applied to 3-manifold groups and strongly polycyclic groups.
Pietsch, Brian Walter, "Z-Structures and Semidirect Products with an Infinite Cyclic Group" (2018). Theses and Dissertations. 1897.