On the Logical Independence of (DR) and (CLA)

Graduate Thesis Or Dissertation

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Citeable URL: https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/w3763f16r

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Attribute Name	Values
Creator	Birnbaum. Dionysus A.
Abstract	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 logical relationships between these flavors of asphericity are known, there remain a few to be answered. In particular, it has long been known that Cohen-Lyndon aspherical (CLA) complexes are not necessarily diagrammatically reducible (DR), but the existence of a (DR) complex which is not (CLA) remains open. We resolve this by showing that the presentation 2-complex associated to the presentation < x,y,t:x=txyx^{-1}y^{-1}t^{-1},y> is (DR) but not (CLA). In fact, we prove that if a nontrivial group G occurs as the fundamental group of a (DR) 2-complex, then there is a (DR) 2-complex with fundamental group $G$ that is not (CLA).
License	All rights reserved
Resource Type	Dissertation
Date Issued	2020-08-28
Degree Level	Doctoral
Degree Name	Doctor of Philosophy (Ph.D.)
Degree Field	Mathematics
Degree Grantor	Oregon State University
Commencement Year	2021
Advisor	Bogley, William A.
Committee Member	Guo, Ren Escher, Christine Schmidt, Tom Pence, Deborah
Academic Affiliation	Mathematics
Rights Statement	In Copyright
Publisher	Oregon State University
Peer Reviewed	No
Language	English [eng]

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