Iterated Peiffer Pairings in the Moore Complex of a Simplicial Group

A pr 1 99 9 Iterated Peiffer pairings in the Moore complex of a simplicial group

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

Applications of Peiffer pairings in the Moore complex of a simplicial group

Applications of Peiffer Pairings in the Moore Complex of a Simplicial Group

Generalising a result of Brown and Loday, we give for n = 3 and 4, a decomposition of the group, dnNGn, of boundaries of a simplicial group G as a product of commutator subgroups. Partial results are given for higher dimensions. Applications to 2-crossed modules and quadratic modules are discussed.

Higher Dimensional Peiffer Elements in Simplicial Commutative Algebras

Let E be a simplicial commutative algebra such that En is generated by degenerate elements. It is shown that in this case the nth term of the Moore complex of E is generated by images of certain pairings from lower dimensions. This is then used to give a description of the boundaries in dimension n 1 for n = 2, 3, and 4.

Higher Dimensional Peiffer Elements in Simplicial Commutative Algebras

Let E be a simplicial commutative algebra such that En is generated by degenerate elements. It is shown that in this case the nth term of the Moore complex of E is generated by images of certain pairings from lower dimensions. This is then used to give a description of the boundaries in dimension n− 1 for n = 2, 3, and 4.