Transversity Physics at Compass

Transverse spin physics is an important part of the scientific programme of the COMPASS experiment at CERN, which started taking data in 2002, scattering 160 GeV/c muon beam on a polarized $^6$LiD target. The analysis of the data taken with the target polarized orthogonally to the muon beam direction has allowed to measure for the first time the Collins and Sivers asymmetries of the deuteron. Both for the positive and the negative hadrons produced in semi-inclusive DIS the measured asymmetries are small and, within errors, compatible with zero: results on part of the accumulated statistics have already been published. Two-hadron asymmetries and $\Lambda$ polarization transfered from the struck quark are also being investigated, and preliminary results on the data collected in the years 2002 and 2003 are given.