Generalized Group Presentations and Formal Deformations of Cw Complexes

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Brown, Richard Arthur

• Mathematics

Identifier

(UMI)AAI8422029

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/71219