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.
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.
