We study transverse-tracefree (TT)-tensors on conformally flat 3-manifolds
(M,g). The Cotton-York tensor linearized at g maps every symmetric
tracefree tensor into one which is TT. The question as to whether this is the
general solution to the TT-condition is viewed as a cohomological problem
within an elliptic complex first found by Gasqui and Goldschmidt and reviewed
in the present paper. The question is answered affirmatively when M is simply
connected and has vanishing 2nd de Rham cohomology.Comment: 11 page
