Shift Dynamics for Cyclically Presented Groups with Length Four Positive Relators Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/6395wd15m

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  • 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 = Gn (x0xkxl) are connected to the finiteness of G and the combinatorial asphericity status of the corresponding cyclic presentation Pn (x0xkxl) that determines G. This dissertation provides an extension of those results to the case where w = x0xjxkxl is a positive word of length four. Additionally, this dissertation provides a complete clas- sification of the cyclically presented groups Gn (x0xjxkxl) that are finite and, except for two families of presentations where the status is unresolved, a complete classification of the cyclic presentations Pn (x0xjxkxl) that are combinatorially aspherical.
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  • description.provenance : Approved for entry into archive by Steven Van Tuyl(steve.vantuyl@oregonstate.edu) on 2017-06-26T23:01:50Z (GMT) No. of bitstreams: 2license_rdf: 1527 bytes, checksum: d4743a92da3ca4b8c256fdf0d7f7680f (MD5)ParkerForrestW2017.pdf: 511874 bytes, checksum: 8146d8eb2bc7bf019d9920f2b9dc70f0 (MD5)
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  • description.provenance : Made available in DSpace on 2017-06-26T23:01:50Z (GMT). No. of bitstreams: 2license_rdf: 1527 bytes, checksum: d4743a92da3ca4b8c256fdf0d7f7680f (MD5)ParkerForrestW2017.pdf: 511874 bytes, checksum: 8146d8eb2bc7bf019d9920f2b9dc70f0 (MD5) Previous issue date: 2017-06-13

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