A turbo compressor including: - a drive shaft including a first axial end portion and a second axial end portion opposite to the first axial end portion , - at least one compression stage configured to compress a refrigerant, the at least one compression stage including at least one impeller connected to the first axial end portion of the drive shaft , - an electrical motor configured to drive in rotation the drive shaft about a rotation axis, the electrical motor including a stator and a rotor , the rotor being connected to the second axial end portion of the drive shaft , - a thrust bearing arrangement configured to limit an axial movement of the drive shaft during operation, - a bearing sleeve located between the electrical motor and the at least one impeller , the bearing sleeve having a longitudinal axis (B) and surrounding the drive shaft , the bearing sleeve including: - a radial gas bearing part which is tubular and which is configured to rotatably support the drive shaft , - a sleeve part surrounding the radial bearing part , the sleeve part including an axial end face which faces towards the at least one impeller and a contact surface which is located at the axial end face and which is configured to cooperate with the thrust bearing arrangement, - an annular gap formed between the radial bearing part and the sleeve part , and - a cooling area formed in an outer circumferential surface of the sleeve part and intended for the passage of a refrigerant so as to dissipate heat from the bearing sleeve , characterized in that the sleeve part includes cuts distributed around the longitudinal axis (B) of the bearing sleeve and emerging into the contact surface . - a drive shaft including a first axial end portion and a second axial end portion opposite to the first axial end portion , - at least one compression stage configured to compress a refrigerant, the at least one compression stage including at least one impeller connected to the first axial end portion of the drive shaft , - an electrical motor configured to drive in rotation the drive shaft about a rotation axis, the electrical motor including a stator and a rotor , the rotor being connected to the second axial end portion of the drive shaft , - a thrust bearing arrangement configured to limit an axial movement of the drive shaft during operation, - a bearing sleeve located between the electrical motor and the at least one impeller , the bearing sleeve having a longitudinal axis (B) and surrounding the drive shaft , the bearing sleeve including: - a radial gas bearing part which is tubular and which is configured to rotatably support the drive shaft , - a sleeve part surrounding the radial bearing part , the sleeve part including an axial end face which faces towards the at least one impeller and a contact surface which is located at the axial end face and which is configured to cooperate with the thrust bearing arrangement, - an annular gap formed between the radial bearing part and the sleeve part , and - a cooling area formed in an outer circumferential surface of the sleeve part and intended for the passage of a refrigerant so as to dissipate heat from the bearing sleeve , <EOS>