  We present reversible magnetization data of a high quality Bi2212 single
crystal and explore the occurrence of 3D-xy critical behavior close to the bulk
transition temperature Tc and of Kosterlitz-Thouless (KT) behavior. Below and
above the presumed Kosterlitz-Thouless transition temperature T_KT we observe
the characteristic 2D-xy behavior: a downward shift of the crossing point
phenomenon towards T_KT as the field is decreased and sufficiently below T_KT
the characteristic 2D-xy relationship between the magnetization an the in-plane
magnetic penetration depth. In contrast, the measured temperature dependence of
the superfluid density does not exhibit the characteristic KT-behavior around
the presumed T_KT. The absence of this feature is traced back to the 2D- to
3D-xy crossover setting in around and above T_KT. Invoking the Maxwell relation
the anomalous field dependence of the specific heat peak is also traced back to
the intermediate 2D-xy behavior. However, close to Tc we observe consistency
with 3D-xy critical behavior, in agreement with measurements of the in-plane
magnetic penetration depth.
