Geodesic
Asphericity and approximation properties of crossed modules
Sbornik. Mathematics, Tome 198 (2007) no. 4, pp. 521-535

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This paper is devoted to the study of the Baer invariants and approximation properties of crossed modules and $\text{cat}^1$-groups. Conditions are considered under which the kernels of crossed modules coincide with the intersection of the lower central series. An algebraic criterion for asphericity is produced for two-dimensional complexes having aspherical plus-construction. As a consequence it is shown that a subcomplex of an aspherical two-dimensional complex is aspherical if and only if its fundamental $\text{cat}^1$-group is residually soluble. Thus, a new formulation in group-theoretic terms is given to the Whitehead asphericity conjecture. Bibliography: 25 titles. 
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     author = {R. V. Mikhailov},
     title = {Asphericity and approximation properties of crossed modules},
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     number = {4},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2007_198_4_a3/}
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R. V. Mikhailov. Asphericity and approximation properties of crossed modules. Sbornik. Mathematics, Tome 198 (2007) no. 4, pp. 521-535. http://geodesic.mathdoc.fr/item/SM_2007_198_4_a3/