A class of groups, called picture groups, is defined. Richard Thompson

s groups
F,
T, and
V are all picture groups. Each picture group is shown to act properly and isometrically on a CAT(0) cubical complex. In particular, all picture groups are a-T-menable.
Keywords CAT(0) cubical complexes - diagram groups - picture groups - Thompson
s groups a-T-menability - Haagerup property
Mathematics Subject Classifications (2000). 20F65, 43A15.