University of Illinois Urbana-Champaign

Generalized Group Presentations and Formal Deformations of Cw Complexes

Brown, Richard Arthur

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https://hdl.handle.net/2142/71219

Description

Title
Generalized Group Presentations and Formal Deformations of Cw Complexes
Author(s)
Brown, Richard Arthur
Issue Date
1984
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(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.
Graduation Semester
1984
Type of Resource
text
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http://hdl.handle.net/2142/71219

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