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Abstract
We consider the flag complex of the well-known rank 4 geometry, associated with the Higman-Sims group HS (i.e., the complex whose vertices are objects of the geometry, and simplices are the flags). The homology of this complex is computed; it equals 0 in dimensions 0 and 1, and Z 2 in dimension 2. These results can be applied to compute the small-dimensional cohomology of HS with coefficient in non-trivial modules.
ACKNOWLEDGMENTS
The author is grateful to I.D.Suprunenko for encouragement.