Category Theory & Homotopy Theory

Iterated Peiffer pairings in the Moore complex of a simplicial group

Abstract:

We introduce a pairing structure within the Moore complex NG of a simplicial group G and use it to investigate generators for NG_n \cap D_n where D_n is the subgroup generated by degenerate elements. This is applied to the study of algebraic models for homotopy types.

ftp access:

xxx-archive : http://uk.arXiv.org/abs/math.AT/9904038

Published in:

Applied Categorical Structures 9 (2001) 111-130.

Free crossed resolutions from simplicial resolutions with given CW-basis

Abstract:

In this paper, we examine the relationship between a CW-basis for a free simplicial group and methods of freely generating the corresponding crossed complex. Attention is concentrated on the case of resolutions, thus comparing free simplicial resolutions with crossed resolutions of a group.

Published in:

Cahiers de Topologie et Geometrie Differentielle categoriques 40 (1999) 261-283.