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Mathematics Preprints 1998


Category Theory & Homotopy Theory

98.07 : EHLERS, P.J. and PORTER, T.

Joins for (augmented) simplicial sets

Abstract:

We introduce a notion of join for (augmented) simnplicial sets generalising the classical join of geometric simplicial complexes. The definition comes naturally from the ordinal sum on the base simplicial category $\Delta$.

Published in:

J Pure and Applied Algebra 145 (2000) 37-44.


98.08 : ARVASI, Z. and PORTER, T.

Freeness conditions for 2-crossed modules of commutative algebras

Abstract:

In this paper we give a construction of free 2-crossed modules. By the use of a `step-by-step' method based on the work of André, we will give a description of crossed algebraic models for the steps in the construction of a free simplicial resolution of an algebra. This involves the introduction of the notion of a free 2-crossed module of algebras.

Published in:

Applied Categorical Structures 6 (1998) 455-471.


98.20 : MUTLU, A. and PORTER, T.

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

Abstract:

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

Published in:

Theory and Applications of Categories 4 (1998) 148-173.


98.21 : MUTLU, A. and PORTER, T.

Freeness conditions for 2-crossed modules and complexes

Abstract:

Using free simplicial groups, it is shown how to construct a free or totally free 2-crossed module on suitable construction data. 2-crossed complexes are introduced and similar freeness results for these are discussed.

Published in:

Theory and Applications of Categories 4 (1998) 174-194.


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