Coexisting with others and interacting in society implies sharing knowledge and attention about world objects, events, features, episodes, and even imagination or abstract ideas in time and space. Inspired by human phenomenological, cognitive and behavioral research, this work focuses on the study of joint attention (JA) for human-robot interaction (HRI), based on two main assumptions: a) the perception and representation of attention jointness constitute an isomorphic relation, and b) inspiration on dynamic neural fields (DNF) theory is a promising way to investigate contextual and non-linear spatio-temporal relations underlying attention and knowledge sharing in HRI. Taking into account the previous considerations, we propose a topology-based model for JA named TOP-JAM, which is able to represent and track in real-time JA states, from observations of behavioral data. More importantly, the model consists in a representation that can be directly understood by human beings, which conforms to robo-ethical principles in social robotics. This study evaluates computational properties of the model in simulation. Through a real experiment with the robot Pepper, the study shows that TOP-JAM is able to track JA in a triad interaction scenario.