On the linear stability of solitons and hairy black holes with a negative cosmological constant: the odd-parity sector

Using a recently developed perturbation formalism based on curvature quanti ties, we investigate the linear stability of black holes and solitons with Yang-Mills hair and a negative cosmological constant. We show that those so lutions which have no linear instabilities under odd- and even-parity spher ically symmetric perturbations remain stable under odd-parity, linear, nons pherically symmetric perturbations.