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Brown, Richard Arthur 2014-12-16T06:18:10Z 2014-12-16T06:18:10Z 10000-01-01 1984 1984 A Peiffer-Whitehead word system W, or generalized group presentation, consists of generators for a free group and words of various orders n (GREATERTHEQ) 2 representing elements of the free group (n = 2), a free crossed module (n = 3) or a free module (n > 3). The P(,n)-equivalence relation on word systems generalizes the extended Nielsen equivalence relation on ordinary group presentations. Word systems, called homotopy readings, can be associated with any connected CW complex K by removing a maximal tree and selecting one word (or generator) per cell, via relative homotopy. Given homotopy readings W(,1) and W(,2) of finite CW complexes K(,1) and K(,2) respectively, we show that W(,1) is P(,n)-equivalent to W(,2) if and only if K(,1) formally (n + 1)-deforms to K(,2). This extends results of P. Wright (1975) and W. Metzler (1982) for the case n = 2. For n = 3, it follows that W(,1) is P(,n)-equivalent to W(,2) if and only if K(,1) and K(,2) have the same simple homotopy type. Made available in DSpace on 2014-12-16T06:18:10Z (GMT). No. of bitstreams: 1 8422029.pdf: 2656175 bytes, checksum: 53e3b849c454045b007ae3e640adf4ea (MD5) Previous issue date: 1984 Embargo set by: Seth Robbins for item 71385 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 106 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1984. http://hdl.handle.net/2142/71219 (UMI)AAI8422029 Mathematics Generalized Group Presentations and Formal Deformations of Cw Complexes text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.