Free crossed resolutions for graph products of groups

2001/01/26 by Ronald Brown, Brown, Ronald, Manuel Bullejos +3
Mathematics · #18G55 #20E99 #20J99 #55U99 #57M15 #Advanced Operator Algebra Research #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GR #msc:18G55 #msc:20E99 #msc:20J99 #msc:55U99 #msc:57M15

paper · pdf · doi:10.48550/arxiv.math/0101220

18 pages, xypic version 2: 20/08/01 Main change is the use of work of H.J. Baues on realisation of morphisms of free crossed resolutions. There are other minor changes 05/07/02 This version includes the work on graph prodducts of groups. For free crossed resolutionds of amalgamated sums and HNN-extensions, see math.AT/0101220. To appear in Proceedings Workshop Korea 2000, Heldermann Verlag

openalex publication_date 2001/01/26 · arxiv created 2002/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The category of crossed complexes gives an algebraic model of the category of CW-complexes and cellular maps. We explain basic results on crossed complexes which allow the computation of free crossed resolutions of graph products of groups, given free crossed resolutions of the individual groups.

Citations

• The Fundamental Groupoid of a Graph of Groups
• Simple Homotopy Types

Related

• Free crossed resolutions of groups and presentations of modules of identities among relations
• Freeness conditions for crossed squares and squared complexes
• Crossed modules and the homotopy 2-type of a free loop space
• Exact sequences of fibrations of crossed complexes, homotopy classification of maps, and nonabelian extensions of groups
• Galois theory, graphs and free groups