Object recognition is a key precursory challenge in the fields of object manipulation and robotic/AI visual reasoning in general. Recognizing object categories, particular instances of objects and viewpoints/poses of objects are three critical subproblems robots must solve in order to accurately grasp/manipulate objects and reason about their environ- ments. Multi-view images of the same object lie on intrinsic low-dimensional manifolds in descriptor spaces (e.g. visual/depth descriptor spaces). These object manifolds share the same topology despite being geometrically different. Each object manifold can be represented as a deformed version of a unified manifold. The object manifolds can thus be parametrized by its homeomorphic mapping/reconstruction from the unified manifold. In this work, we construct a manifold descriptor from this mapping between homeomorphic manifolds and use it to jointly solve the three challenging recognition sub-problems. We extensively experiment on a challenging multi-modal (i.e. RGBD) dataset and other object pose datasets and achieve state-of-the-art results.