Diagram groups and directed 2-complexes : homotopy and homology

  title={Diagram groups and directed 2-complexes : homotopy and homology},
  author={Victor S. Guba and Mark V. Sapir},
We show that diagram groups can be viewed as fundamental groups of spaces of positive paths on directed 2-complexes (these spaces of paths turn out to be classifying spaces). Thus diagram groups are analogs of second homotopy groups, although diagram groups are as a rule non-Abelian. Part of the paper is a review of the previous results from this point of view. In particular, we show that the so called rigidity of the R. Thompson’s group F and some other groups is similar to the flat torus… CONTINUE READING


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