In this paper, we present a unified model for the automatic induction of word senses from text, and the subsequent disambiguation of particular word instances using the automatically extracted sense inventory. The induction step and the disambiguation step are based on the same principle: words and contexts are mapped to a limited number of topical dimensions in a latent semantic word space. The intuition is that a particular sense is associated with a particular topic, so that different senses can be discriminated through their association with particular topical dimensions; in a similar vein, a particular instance of a word can be disambiguated by determining its most important topical dimensions. The model is evaluated on the semeval-2010 word sense induction and disambiguation task, on which it reaches state-of-the-art results.