A floating structure comprising a hull including bearing walls (3, 5, 7) defining a polyhedral space inside the hull, the floating structure comprising a sealed and thermally insulated tank housed in the polyhedral space to store a low-temperature liquefied gas, in which an upper bearing wall (7, 107) of the hull has an opening and bears a turret-like cargo tank dome (15, 21, 221) projecting from an exterior surface of the upper bearing wall around the opening, the opening and the turret-like cargo tank dome being intended for the passage of cargo handling equipment (16, 22, 222) for handling a liquid phase and/or a vapor phase of the liquefied gas contained in the tank, in which the tank comprises a plurality of tank walls fixed to the bearing walls of the hull, in which an upper tank wall comprises a multilayer structure fixed to an interior surface of the upper bearing wall, the multilayer structure being formed of a primary sealing membrane (13, 113, 213) intended to be in contact with the liquefied gas contained in the tank, a secondary sealing membrane (11, 111, 211) arranged between the primary sealing membrane and the upper bearing wall, a secondary insulating barrier (10, 110, 210) positioned between the secondary sealing membrane and the upper bearing wall, and a primary insulating barrier (12, 112, 212) positioned between the secondary sealing membrane and the primary sealing membrane, the floating structure further comprising a primary venting device (25, 125) comprising a primary venting pipe (I, Q), a secondary venting device (35, 135) comprising a secondary venting pipe (K, S), a gas reservoir (41, 141) containing a tracer gas that is non-condensable or that has a condensation temperature below the low temperature of the liquefied gas contained in the tank, a gas detector (43, 143) able to detect the tracer gas, characterized in that the turret-like cargo tank dome comprises: an internal fluidtight wall forming a sheath (113, 222) engaged through the opening of the upper bearing wall (7, 107, 207) and connected in a fluidtight manner to the primary sealing membrane (13, 213) of the upper tank wall all around the sheath, an external fluidtight wall (103, 32) arranged around the sheath some distance from the sheath parallel to the sheath, the external fluidtight wall being connected in fluidtight manner to the upper bearing wall around the opening, a dividing wall (111, 60, 61) arranged between the external fluidtight wall (103, 32) and the internal fluidtight wall (113, 222) of the turret-like cargo tank dome and dividing the space defined between the external fluidtight wall and the internal fluidtight wall of the turret-like cargo tank dome into, on the one hand, a secondary space (110, 62, 64) communicating through the opening of the upper bearing wall with the secondary insulating barrier (10, 210) of the upper tank wall arranged around the opening and, on the other hand, a primary space (112, 60, 61) communicating through the opening of the upper bearing wall with the primary insulating barrier (12, 212) of the upper tank wall positioned around the opening, the primary venting device (25, 125) comprising a primary overpressure relief valve (27, 127), the primary venting pipe (I, Q) communicating directly with the primary space of the turret-like cargo tank dome and passing through the external fluidtight wall of the turret-like cargo tank dome in order to allow gas to be vented from the primary space in response to an opening of the primary overpressure relief valve, the secondary venting device (35, 135) comprising a secondary overpressure relief valve (37, 137), the secondary venting pipe (K, S) communicating directly with the secondary space of the turret-like cargo tank dome and passing through the external fluidtight wall of the turret-like cargo tank dome to allow gas to be vented from the secondary space in response to an opening of the secondary overpressure relief valve, the gas reservoir being connected via a control valve (42, 142) to one of the venting devices that are the primary venting device and the secondary venting device, and the gas detector being in communication with the other of the venting devices that are the primary venting device, notably the primary venting pipe, and the secondary venting device, notably the secondary venting pipe. an internal fluidtight wall forming a sheath (113, 222) engaged through the opening of the upper bearing wall (7, 107, 207) and connected in a fluidtight manner to the primary sealing membrane (13, 213) of the upper tank wall all around the sheath, an external fluidtight wall (103, 32) arranged around the sheath some distance from the sheath parallel to the sheath, the external fluidtight wall being connected in fluidtight manner to the upper bearing wall around the opening, a dividing wall (111, 60, 61) arranged between the external fluidtight wall (103, 32) and the internal fluidtight wall (113, 222) of the turret-like cargo tank dome and dividing the space defined between the external fluidtight wall and the internal fluidtight wall of the turret-like cargo tank dome into, on the one hand, a secondary space (110, 62, 64) communicating through the opening of the upper bearing wall with the secondary insulating barrier (10, 210) of the upper tank wall arranged around the opening and, on the other hand, a primary space (112, 60, 61) communicating through the opening of the upper bearing wall with the primary insulating barrier (12, 212) of the upper tank wall positioned around the opening,