Study of nucleon spin structure with a transversely polarized target in COMPASS

The nucleon spin structure is studied in COMPASS at CERN by the measurement of the double spin asymmetry of the semi inclusive deep inelastic scattering of a polarized muon at 160 GeV/c off a polarized $^{6}$LiD target. The target can be polarized transversely, as well as longitudinally, with respect to the longitudinally polarized muon beam. This allows the measurement of the Collins and Sivers asymmetries and two-hadron production asymmetries. The Collins and the two-hadron production asymmetries have a connection to the transverse spin distribution function $\Delta _T q\left( x \right)$ , referred to as transversity. Approximately 20{\%} of the beam-time in 2002, 2003 and 2004 was spent in the transverse configuration. The preliminary results of the analysis of the data obtained in 2002 and 2003 are presented.