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Title:  Generalized Group Presentations and Formal Deformations of Cw Complexes 
Author(s):  Brown, Richard Arthur 
Department / Program:  Mathematics 
Discipline:  Mathematics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Mathematics 
Abstract:  A PeifferWhitehead 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. 
Issue Date:  1984 
Type:  Text 
Description:  106 p. Thesis (Ph.D.)University of Illinois at UrbanaChampaign, 1984. 
URI:  http://hdl.handle.net/2142/71219 
Other Identifier(s):  (UMI)AAI8422029 
Date Available in IDEALS:  20141216 
Date Deposited:  1984 
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Dissertations and Theses  Mathematics

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois