Christopher D. Wensley

Computation and homotopical applications of induced crossed modules

We explain how the computation of induced crossed modules allows the computation of certain homotopy 2-types and, in particular, second homotopy groups. We discuss various issues involved in computing induced crossed modules and give Some examples and applications.

ENUMERATION OF CAT1-GROUPS OF LOW ORDER

In this paper we describe a share package

Crossed Complexes, and Free Crossed Resolutions for Amalgamated Sums and HNN-Extensions of Groups

\mathsf {XMOD}

Complete involutive rewriting systems

of functions for computing with finite, permutation crossed modules, cat1-groups and their morphisms, written using the

Automorphisms and Homotopies of Groupoids and Crossed Modules

\mathsf {GAP}

String rewriting for double coset systems

group theory programming language. The category XMod of crossed modules is equivalent to the category Cat1 of cat1-groups and we include functions emulating the functors between these categories. The monoid of derivations of a crossed module

On infinite induced crossed modules and the homotopy 2-type of mapping cones.

{\mathcal X}

Graphs of morphisms of graphs

, and the corresponding monoid of sections of a cat1-group

Groups St Andrews 2001 in Oxford: Logged rewriting and identities among relators

{\mathcal C}

Logged Rewriting Procedures with Application to Identities Among Relations

, are constructed using the Whitehead multiplication. The Whitehead group of invertible derivations, together with the group of automorphisms of