This talk gave a sketch of the contents and background to a book with the titleNonabelian
algebraic topology'being written under support of a Leverhulme Emeritus Fellowship (2002 …

Groupoids and crossed objects in algebraic topology Introduction Page 1 Homology, Homotopy
and Applications, vol.1, No.1,1999, 1-78. Groupoids and crossed objects in algebraic topology …

In 1988, Brown and Ellis published [3] a generalised Hopf formula for the higher homology
of a group. Although substantially correct, their result lacks one necessary condition. We …

On the Asphericity of Length Four Relative Group Presentations. Sign In Folder Preferences
Languages New Features! Help Exit New Search Publications Subject Terms Cited References …

A 2-complex X is Cockcroft if the Hurewicz map. rr2X+ H2X is zero. WH Cockcroft [9]
considered the effect on the image of the Hurewicz map of adding 2-cells to a 2-complex X …

WA Bogley and MA Gutierrez [2] have recently obtained an eight-term exact homology
sequence that relates the integral homology of a quotient group Г/MN, where M and N are …

A combinatorial hypothesis is presented that serves as a necessary and sufficient condition
for a union of connected Cockcroft two-complexes to be Cockcroft. This combinatorial …

The Peiffer product of groups first arose in work of JHC Whitehead on the structure of relative
homotopy groups, and is closely related to problems of asphericity for two-complexes. We …

We show that the intersection of three subgroups in a free group is related to the
computation of the third homotopy group π3. This generalizes a result of Gutierrez–Ratcliffe …

This paper is based on the doctorial dissertation of the author. Most of its results were
exposed in monograph [1] and in other works of the author. The main objects of study in this …