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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 Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
Abstract: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.
Issue Date:1984
Type:Text
Description:106 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1984.
URI:http://hdl.handle.net/2142/71219
Other Identifier(s):(UMI)AAI8422029
Date Available in IDEALS:2014-12-16
Date Deposited:1984


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