We study the two transverse quadrupole modes of a cigar-shaped Bose-Einsteincondensate with a single centered vortex. We show that the counter-rotatingmode is more strongly damped than in the absence of a vortex, whereas theco-rotating mode is not affected appreciably by the vortex. We interpret thisresult as a decay of the counter-rotating quadrupole mode into two excitationsof the vortex line, the so-called Kelvin modes. This is supported by directobservation of the wiggling vortex line.
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