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CREATED:20250725T141802Z
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SUMMARY:PhD Dissertation Defense: Mr. Joe Paulson
DESCRIPTION:Theory of Z_n – Structures\nMr. Joe Paulson\nGraduate Student\nUniversity of Wisconsin-Milwaukee \nIn this defense\, we discuss the boundaries of Type F_n groups; those being groups whose K(G\,1) complex has a finite n-skeleton. The boundaries we develop extend the notion of Z-boundaries to what we call Z_n-boundaries. This extension centers around groups no longer acting geometrically on contractible spaces\, but instead n-connected spaces. Immediately this means the major theorems of “Boundary Swapping” and “Shape Equivalence of Z-Boundaries” will need revision\, but a more subtle point to be discussed is that the category of spaces must also be generalized. \nAfter discussing the foundation work for a theory of Z_n-boundaries\, we end with an exploration how these new structures can be related to other well-known compactifications such as the one-point compactification\, end-point compactification\, and Z-compactifications. \nAdvisor:\nCraig Guilbault \nCommittee Members:\nBoris Okun\, Chris Hruska\, Jonah Gaster\, and Pamela Harris
URL:/math/event/phd-dissertation-defense-mr-joe-paulson/
LOCATION:EMS Building\, Room E408\, E408; 3200 N Cramer St.\, Milwaukee\, WI\, 53211\, United States
CATEGORIES:Graduate Student Defenses
ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu
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