In traditional Distributional Semantic Models (DSMs) the multiple senses of a polysemous word are conflated into a single vector space representation. In this work, we propose a DSM that learns multiple distributional representations of a word based on different topics. First, a separate DSM is trained for each topic and then each of the topic-based DSMs is aligned to a common vector space. Our unsupervised mapping approach is motivated by the hypothesis that words preserving their relative distances in different topic semantic sub-spaces constitute robust semantic anchors that define the mappings between them. Aligned cross-topic representations achieve state-of-the-art results for the task of contextual word similarity. Furthermore, evaluation on NLP downstream tasks shows that multiple topic-based embeddings outperform single-prototype models.